The Ganges is one of the greatest rivers on Earth, but it is dying.

From the icy Himalayan peaks, where it begins, right down to the Bay of Bengal, it is being slowly poisoned.

The Ganges is revered in India but it is also the sewer that carries away the waste from the 450 million people who live in its catchment area.

Pollution from the factories and farms of the fastest-growing large economy in the world – and from the riverside cremation of Hindu true believers - has turned its waters toxic.

The Indian Prime Minister, Narendra Modi, promised two years ago to clean up the Ganges, but can he do it?

Can the sacred mother of Hinduism be saved?

The source of the Ganges lies among the soaring, snow-clad peaks of the Himalayas.

As a rose-pink dawn rises over the jagged teeth of the mountains, the valley where the river begins remains in deep shadow.

It takes hours for the sun to scale the great crags. Only then does a single shaft of sunlight finally penetrate into the chasm.

It strikes a glacier called Gangotri, suddenly illuminating its cloudy blue and white depths.

It is easy to understand why this is one of the most sacred sites in all Hinduism. Up here in the cold fresh air the great shimmering body of frozen water appears radiantly pure.

At the foot of the glacier there is a cave in the ice. This is “Gaumukh”, the cow’s mouth, and the chuckling stream of crystal clear icy water that emerges from it is the beginning of the Ganges.

Ma Ganga, it is known in Hindi: “Mother Ganges”. It’s an apt name - the Ganges has nurtured and supported the rise of Indian civilisation.

As the stream snakes down from the mountains it gathers pace and volume, joined by hundreds of others bringing snowmelt from the vast Himalayan watershed.

But studies show that even here in the Himalayas the water is becoming increasingly polluted.

And the further you descend, the more pronounced the legendary river’s problems become.

In the holy city of Rishikesh, Swami Chidanand Saraswati is leading the evening aarti, a Hindu fire ceremony.

He is an irrepressibly cheerful man, the flickering light of the butter candles he circles in front of him twinkle in his eyes as he chants and sings along with the music. About 50 monks take part, watched by a couple of hundred devotees.

These river aartis are a celebration of the Ganges. A similar ritual is performed in towns and villages all along the 2,500km-long (1,500-mile) river.

All day pilgrims have been descending to the water to bathe, part of an ancient ritual of purification.

Hindus revere the Ganges as a god. They believe she came down from heaven to cleanse the Earth, and that bathing in her waters can wash away a person’s sins.

The Swami has built the ashram into a huge enterprise. He glances down modestly when I ask how many followers he has. “Perhaps a million,” he replies. But his demeanour changes when I ask about pollution in the river. His brow furrows.

Too many people think the Ganges not only purifies sin but also has the power to cleanse itself, he says.

“People think Ganga can take care of my sins, can take care of anything, and they forget that while Ganga can take care of your sins it cannot take care of your waste, of your pollution.”

Campaigning for a serious effort to clean the river, he says, occupies most of his time. He is in no doubt that India is killing the Ganges, “killing its own mother”, he says, and he is determined to save her.

The prime minister, Narendra Modi, a Hindu nationalist, also sees cleaning up the Ganges as nothing less than a mission from God.

“Ma Ganga has called me,” he told the crowd at his victory celebration, when he was swept to power in a landslide victory two years ago.

“She has decided some responsibilities for me. Ma Ganga is screaming for help, she is saying I hope one of my sons gets me out of this filth,” he said. “It is possible it has been decided by God for me to serve Ma Ganga.”

He has pledged serious money to his Clean Ganga Mission - more than $3bn (£2bn) over five years.

Quite deliberately he has chosen this as one of his signature projects, knowing that it is symbolic of an even bigger challenge - India’s effort to lift its people out of poverty and to become a modern world power.

Previous Indian leaders launched similar initiatives. In the 1980s Rajiv Gandhi began a huge programme of public works, building sewers and water treatment plants, for example.

But they didn’t solve the problem. In fact, the Ganges has steadily become more and more polluted.

So what can be done?

Rakesh Jaiswal believes he has a good idea where to begin.

The veteran environmental campaigner has told me to meet him in the industrial area of Kanpur.

Kanpur is the centre of India’s vast leather industry, and Jaiswal believes it is the dirtiest city in the entire country.

Most of the leather produced in Kanpur is exported, much of it to Europe and the US. More likely than not you own products that use leather from Kanpur.

“Follow me,” he orders, before vanishing into a web of high-walled alleyways.

This modest, plump man has pretty much single-handedly led the campaign to clean up the leather industry in his home city for more than two decades.

We swerve around a couple of tight corners until the alleyway opens up into a broad brick-paved path beside a stream.

Jaiswal turns to speak to me. I see he has a handkerchief clamped over his nose and is gesturing to the dark black water.

I don’t hear a word he says.

I am totally overwhelmed - disabled - by the warm oily stench coming from the water.

The smell is impossible to describe. There’s human waste in there, and something very rotten indeed.

But that’s just what a wine buff would call the “top notes”. Behind them are other awful odours that I can’t even begin to identify: meaty, acidic and very wrong.

Instinct takes over. I begin to retch uncontrollably. And each time my body convulses I suck in another great lungful of that fetid air.

It is only with great effort that I manage to avoid vomiting.

Jaiswal leads me swiftly away to a bluff overlooking the place where this filthy drain flows directly and completely unfiltered into the main flow of the Ganges.

There is sewage and other domestic waste in the stream, he tells me, but also much more dangerous stuff.

The leather industry uses highly toxic chemicals to soften and preserve the hides, he says. Some - including compounds of chromium - are powerful carcinogens.

“India has the resources to clean up the river,” he tells me.

As Jaiswal sees it, the problem is simple. The government just does not enforce the laws it has enacted.

What about the huge emphasis Narendra Modi has put on this project, I want to know.

“Maybe he didn’t realise how difficult it would be,” he says.

“It doesn’t matter how many meetings Modi has held in the past, how many he is holding, or will be holding in the future, I need to see the change on the ground to believe something is happening.”

I can’t remember ever meeting a more dispirited campaigner.

“I don’t think I am ever going to see a healthy and clean river in my lifetime. For the last 22 years I’ve been watching the same polluted river and there has been no change. So much I have done, so much the government has done, but nothing has changed. All hope is dead for me now.”

At the Water Ministry in Delhi I am surprised to learn that the civil servant in charge of the Clean Ganga mission, Shashi Shekhar, agrees with Jaiswal’s diagnosis that corruption and mismanagement have allowed pollution to pour into the river.

He quotes figures which show that, until recently, there were almost 200 tanneries operating in Kanpur without licences. Like Jaiswal, he says this could only happen with the connivance of corrupt officials.

But he says things really are changing.

The government has tightened up the rules, he says - every tannery now has to install its own effluent treatment and chromium recovery plants, for example - and it has also improved enforcement.

More than 100 tanneries have been shut down, Shekhar tells me, because they didn’t meet the new standards.

It takes a lot of wheedling, but eventually we get permission to go out with pollution control officers on one of their surprise inspections.

The first tannery they take me to is a model of hygiene and efficiency. So much so, it makes me suspicious. I ask if I can choose where we go next, and to my surprise, they agree.

There are more than 400 tanneries in Kanpur and I pick one at random. As soon as the security guard creaks opens the big iron gate it is clear this is a very different operation.

Someone shouts and we see a scuffle at the end of the long yard. They seem to be trying to turn off the machines. We rush down.

What we find is truly horrific.

Leather tanning - even at the best of times - is not a pleasant process. First you have to scrape any remaining flesh from the hides. It seems they’ve been doing that here for days, but haven’t got round to cleaning up.

Beside a machine, a huge mound of rotten meat spills out on to the floor of the workshop. It is four days’ worth, one of the workers tells the inspector. And this is at a temperature of 30C (86F).

But I’m more worried by the blue-tinted water sloshing out of one of the great rotating wooden drums they use to process the hides. It was this they were trying to turn off.

That blue, the pollution inspector says, is the signature colour of the most dangerous of all the chemicals used in the tanning process, chromium.

He says the contaminated liquid is not going into the public drainage system, it is contained within the effluent treatment system of the tannery, but that it is not good practice to have so much washing around.

“I will recommend this place is closed,” the inspector tells me earnestly as we leave.

As he and his team walk off down the lane I’m left feeling confused.

He seems sincerely to want to clean up the industry, and appears to be empowered to do so, but how many of Kanpur's tanneries are like this one, and how come the effluent entering the river is so disgusting?

Cleaning the Ganges isn’t just a question of controlling what is going into the river, but also a question of controlling what is being taken out.

The river is a crucial source of water for a vast area. Its basin covers more than one million sq km (390,000 sq miles) and is home to more than 40% of India’s 1.3 billion-strong population.

All along the length of the river you see channels siphoning the flow for irrigation and for drinking water. Most of Delhi’s water, for example, comes to the city in two great canals, one from the Ganges and the other from one of its main tributaries, the Yamuna.

And the water taken directly from the main flow is just one part of the problem. More worrying still is the water that is taken from the ground.

The vast plains either side of the Ganges are the breadbasket of India. These hugely fertile flatlands have produced the food that has sustained India for millennia.

The rich alluvial soil is very productive, so long as farmers keep it well irrigated, says Rajesh Bajpai of the WWF.

He’s another passionate campaigner and has spent more than two decades working with farmers on these plains.

His mission: to reduce the amount of water they use.

It doesn’t take long to dig a well here. The water is just 100m (330ft) or so down, so a team can do it in a couple of days of hot, hard labour - I should know, I helped dig one.

Once the well is dug, there is no restriction on how much water farmers can take. The only limit is the cost of the fuel needed to pump it out of the ground.

And since virtually every one of the more than two hundred million farmers in the plain of the Ganges now has a well, vast amounts of water are being used. As a result, say hydrologists, the water table is falling, in some places very dramatically.

In 2012 scientists at India’s National Geophysical Research Institute said Delhi’s groundwater could dry up in just a few years.

So much water is now being taken that some once free-flowing parts of the river are now sluggish or even stagnant during the dry months - effectively they have become nothing more than an open sewer.

It doesn’t help that the country is in the grip of a devastating drought after the failure of the monsoon for two years in a row.

But Bajpai believes he has at least the beginnings of a solution.

He leads me across the fields and shows me a magnificent old diesel engine with a huge cast-iron flywheel.

A farmhand cajoles it into life and it emits a series of throaty coughs, puffing out filthy clouds of diesel smoke. The thick hose attached to it throbs and swells as the pump begins to suck up water from deep underground.

I follow the hose down the lane and into the next field, where the cool, clean water the pump is drawing out pours into one of the neat little sections the farmer, Shri Ram, has created by heaping up the muddy soil of the field into a series of dams.

As each section is flooded, he breaches the dam wall and floods another.

It turns out that this system is far more effective than flooding the whole field at once.

“We used to use lots of water before, now we irrigate the fields with much less,” the farmer says.

It is a pleasure to see how proud Ram is of his efforts.

“All the other farmers are also doing it,” he says. “It is good for everybody. We spend less on water and get good yields and that means we save money.” He smiles broadly.

Similar water-saving efforts are now being replicated across India but many economists believe that a more fundamental solution is needed.

They argue that farmers need to be incentivised to value water properly.

That would mean stripping away the plethora of subsidies, in particularly those that support the cultivation of water-intensive crops such as sugar cane and cotton.

Or - more radical still - farmers could actually pay for the water they use.

But that is very unlikely to happen.

With two-thirds of the Indian population still dependent on agriculture, farmers are a crucial political constituency, and one Indian politicians are careful to cultivate.

No city embodies India like Varanasi.

This is the “Incredible India” you see in the adverts - noisy, chaotic, colourful, rich with tradition, and radiantly beautiful.

But what really overwhelms visitors is the number of people. There are people everywhere. And that’s another big challenge the clean-up campaign faces: the sheer scale of the problem.

Just try to walk through the tangle of lanes alongside the ghats - the series of stone platforms and steps that lead down to the Ganges – and you are caught up in another great river, a river of people.

Fires flicker day and night at the two “burning ghats”, where the ancient practice of riverside cremation still continues.

Hindus believe that being burned on a pyre beside the Ganges brings moksha: liberation from the cycle of death and rebirth.

It is reckoned that 32,000 human corpses are cremated here each year with up to 300 tonnes of half-burnt human flesh released into the Ganges.

But that is only a tiny part of the pollution problem.

The real issue here, as along the entire length of the river, is the waste from all those living humans.

The Ganges is still the main sewer for many of the 450 million people reckoned to live in its catchment area.

The first Ganges action plan 30 years ago commissioned a series of huge sewage plants. The plants are still there but, according to the government’s own figures, most are working way below capacity or not working at all.

Sanjay Kumar Singh, who runs the Ganga Pollution Control Unit at Varanasi, is a man who understands the ebb and flow of filth in his city.

“The total treatment capacity is 100 million litres a day, but 300 million litres is being generated,” he says solemnly.

The figures elsewhere are even worse, according to the Centre for Science and the Environment, an Indian research and campaigning organisation. It estimates that 80% of sewage in the Ganges basin is untreated.

Which is why faecal contamination in the river is so high.

Here in Varanasi it is sometimes more than 150 times the recommended safe level for bathing, yet vast numbers of people bathe away regardless.

And that brings us to the most compelling reason of all to clean up the river. In India today a third of a million children under five still die each year from diarrhoea.

The man whose job is to oversee Narendra Modi’s ambitious clean-up plan has an office in one of the greenest buildings in India. Or at least that’s what the posters at the Environment Ministry claim.

Apparently it is a passive building - it doesn’t need power for heating or cooling - and has an impressive array of solar panels on the roof.

But there is nothing passive about Prakesh Javadekar, the Indian Environment Minister. He is a lively man, with a neat little beard.

The prime minister sits in on the committee that oversees the Clean Ganga Mission, but Javadekar runs the show day to day.

As a project, cleaning the Ganges dwarfs the attempts to clean other rivers such as the Thames or the Rhine. It is on a far larger scale, and involves many more people.

So I want to know why, after so many other attempts to clean the Ganges have failed, Modi’s government believes it can do better.

“Because we have learned lessons from their mistakes,” says Javadekar with a confident smile. He tells me Modi is leading from the front.

He says every aspect of the pollution problem has been mapped out, and the government has worked out how to deal with it in what he calls a “time-bound manner”.

He talks about the new regulations on industrial units, knows how many tanneries have been closed down and claims industrial pollution has already fallen by a third. He says new effluent treatment plants will be built and that corruption will not be a problem - every rupee the government spends will be accounted for.

As he cheerfully reels off the government’s plans it finally dawns on me why he is so upbeat.

The government has set itself tough targets and, to be fair, assigned a decent budget to the world’s biggest river-cleaning project - but for the moment he is sheltered by the sheer scale of what his government is attempting to do.

“We are not saying that the whole Ganga mission will be complete in five years, no. Five years will ensure there is a marked difference but this is a long project,” he says.

“The Rhine and the Thames were in the same dirty state 50 or 60 years ago and it took nearly 20 years to change the overall ecology of that, and we will also achieve it within 10 to 15 years’ time.”

As I leave the Environment Ministry I can’t help feeling a little deflated.

I had been looking forward to a good confrontational interview but I have to concede that the minister’s position is reasonable - it is too early to judge the government’s record.

Nevertheless, given the state of the river and history of efforts to improve it, it is hard to be optimistic.

It takes something very special to give me any sense of optimism about the Ganges.

This begins with a tantalising invitation from contacts at the WWF, who ask if I want to try to get a glimpse one of the rarest species in India, the Ganges river dolphin.

These extraordinary animals are to all intents and purposes blind - they have evolved a system of echolocation to navigate and catch fish in the murky waters of the Ganges.

But they are threatened with extinction. Back in the 1980s the population was reckoned to have fallen to just 5,000 in India.

According to a recent survey by WWF there are now fewer than 2,000 left, and that figure is higher than the experts were expecting.

When I mention my dolphin-watching ambitions to a grizzled fellow journalist over a large Black Dog whisky at the picturesquely decrepit foreign correspondents’ club in the centre of Delhi, he meets them with a derisive snort.

“Not only are they very rare, but they aren’t nearly as frisky as their maritime cousins,” he warns. “You’ll be lucky to see anything more than a grey dorsal fin break the surface.”

My hopes suitably quashed, I await further details from WWF.

I’m expecting that we’ll be heading to the higher reaches of the river where the water is cleanest but they tell me to meet them in Allahabad.

The city is on one of the most polluted stretches of the Ganges of them all, just downstream from Kanpur.

With a camera crew, I drive to a little village. We have been told to get there by 10:00 because the dolphins are most active in the morning.

I’m prepared for a long wait, but as I walk down a steep slope on to the sandy banks beside the river I see something break the surface.

“That wasn’t a dolphin was it?” I ask, astonished.

It was, Asghar Nawab of WWF tells me. He explains that the dolphins need to breathe every minute or two, so when a pod - a dolphin family - is around they come to the surface very regularly.

But it is one thing to see dolphins, quite another to get good pictures of them.

Fortunately the excellent BBC cameraman, Sanjay Ganguly, is up to the task. And he is ably assisted by the dolphins themselves, which jump and splash in the water, just as playfully as those in the oceans.

I will never forget one moment when seven dolphins jump near the boat, one after the other.

After a couple of hours on the river we’ve bagged some wonderful shots of these incredible animals.

I am surprised what an impression it makes on me.

It tells us that, despite the pollution, the river is capable of supporting these amazing animals.

It also demonstrates again why it so important that the Indian government’s efforts to clean up this river succeed.

My final destination is Gangasagar, on the Bay of Bengal where the Ganges meets the Indian Ocean.

This is another holy site and I visit during the annual mela, when the descent of Ganga from heaven is celebrated.

More than a million people have come here to bathe in the holy but polluted waters. That sounds like a lot, but by the standard of Ganges festivals it is quite modest.

Some 120 million people are reckoned to have visited Allahabad over a two-month period in 2013 for the Maha Kumbh Mela - a celebration held once every 12 years.

More than 30 million are estimated to have visited on one day alone - 10 February 2013.

These huge numbers are a measure of just how important the Ganges is to Hindus, and explains why the Clean Ganga Mission has been given such prominence by the government.

The prime minister, Narendra Modi, knows it is a key yardstick by which his success or failure will be judged.

His efforts to clean the Ganges are a test of India’s ability to modernise - to tackle corruption and introduce proper regulation, as well as to invest massively in waste treatment.

But he has a crucial asset - the fact that so many Indians want him to succeed.

On the banks of the Ganges I meet Swami Chidanand again, the cheerful religious leader I met way back in Rishikesh. He believes change will come.

“I think one day we will see the Ganga - the pristine Ganga - and this will happen not only because the politicians but people also, all stakeholders will come together. Because rivers belong to all, Ganga belongs to all. We all must come together. I’m very optimistic, we will see it through.”

Let’s hope so. Because if India can clean up one of the dirtiest rivers in the world, who knows what else this great rising nation can achieve?