Next up is Labour leader Jeremy Corbyn.

"The reality is, we are leaving the European Union," he says, calling for better support for big UK industries as a result of the negotiations.

He accepts the UK cannot remain in the EU single market and will need to develop a new set of trading relationships, predicting this will be "very complicated".

BBC Radio 5 live

5 live’s reporters have been out and about across the UK, finding out how people are feeling on the day Article 50 is triggered. From a farm on Derbyshire to a tech company in Swansea, this is what people told us.

Image source, AFP

Asked about the "Brexit dividend" promised by the Leave campaign before the referendum, Theresa May. who backed the rival campaign to stay in the EU, says the UK will be able to decide how it spends "significant sums" currently given to the EU.

Will it go to the NHS, as promised by Vote Leave? "During the referendum there were points made, often very passionately, on both sides of the argument," she says.

"We are now beyond the referendum, we are now at the stage where we are putting this into practice."

Theresa May tells Andrew Neil she wants to keep the same level of co-operation on cross-border security issues after the UK has left the EU.

This has emerged as a talking point following her Article 50 letter, which suggests crime and security co-operation could suffer if Brexit talks fail to reach agreement.

Watch her answer here

How about the government's comments that the UK could change its "economic model" to stay competitive if no trade deal is reached? ( read more here )

Labour have taken this as a threat to turn the UK into a tax haven, but the PM tells Andrew Neil this amounts to a "straw man argument".

"What it's about is making sure that jobs stay in the UK and new jobs are created here in the UK," she says.

Theresa May says she is confident all the talks can be wrapped up inside two years. Under Article 50, the UK will leave the EU at this point unless both sides agree to an extension of negotiations.

"It's in both sides' interests to do this," the PM says.

Mrs May says that because the UK has been part of the EU makes it easier to reach agreement than "if we were coming at it completely fresh".

Theresa May says she wants trade between the UK and the EU to be "as frictionless and tariff-free as possible".

She says the UK will have a "different relationship" with the EU after Brexit, but that it will "have the same benefits" on trade.

Watch this section back

Reality Check

The prime minister says she wants a reciprocal agreement on the rights of the EU citizens in the UK and the UK citizens in the EU as early as possible.

The mood in Brussels is similar: sorting out the rights of the 3.16m EU citizens, external who live here and about 900,000, external UK passport holders who live in the EU is a priority there too.

But the reciprocal deal will be complex and will have to cover things like access to healthcare and pensions.

Reality Check

Andrew Neil has been asking about the possibility of the UK having to pay a £50bn exit fee on leaving the EU.

The prime minister wouldn’t discuss figures and stressed that people had voted to stop making large annual payments to the EU. But she didn’t rule out paying an exit fee and she said the UK is a law-abiding nation and that the government would have to look at what its obligations are.

She also said there had been no formal demands, which is not surprising as the official negotiations have not yet started.

Here’s a Reality Check on where that figure comes from. 

Andrew Neil asks Theresa May about one of the key themes of the EU referendum - immigration. Will there be a reduction in the numbers, he asks.

"We will see a difference in the numbers coming in," replies the PM.

She says the government will be able to have control and "set the rules" but won't go into detail about the new model, saying a new bill will be brought forward "in due course".

Reality Check

Image source, Getty Images

Theresa May has been talking about net migration to the UK, which her party aspires to get below 100,000 a year.

The figure is still well over that level, dipping under 300,000 in the year to September 2016 , although the figures are imprecise, as we discussed in this Reality Check .

Starting now on BBC One - Andrew Neil is interviewing Theresa May, Jeremy Corbyn and other party leaders about Brexit. Watch Brexit: What Next? here.

Eleanor Garnier
Political Correspondent

There was loud banging on the tables in support of Theresa May as she went into the meeting of the 1922 committee and again when she left.

After the meeting one senior Tory MP said Mrs May told the gathering that "the task starts now and there's lots of work to do" and she apparently added there are "opportunities for everyone" saying the "referendum was not just about Brexit but about everyone who felt left behind". 

"She was great" one MP said as he left, another added she was "good, very good".

James Landale
Diplomatic correspondent

In the next few days, the EU will publish a holding statement setting out its initial, draft response to Mrs May's letter.

This document - several pages long - will make clear the EU's key principles for the talks ahead. But its formal negotiating position will be agreed only at a summit of the remaining 27 member states at the end of April, so face-to-face discussions are unlikely until May or even early June, well after the French presidential elections.

There'll be an early row over whether or not Britain's exit deal and future trading relationship with the EU are discussed at the same time or one after another.

There'll be an even bigger row over what outstanding debts the UK may have to pay when it leaves.

Theresa May promised today a "fair settlement". The EU wants £50bn. And there'll also be early talks about the rights of EU citizens living in the UK and Britons in the EU: politically easy; technically very hard.

And as for discussions about any future trade deal, most people expect those will not start until well into the autumn, certainly not before the German elections in September. The hope is that a final Brexit deal could be agreed by October next year so there's time for it be ratified by EU parliaments before the UK leaves in March 2019. That at least is the hope.

Canadian Prime Minister Justin Trudeau has said the UK will remain a "great friend and ally and economic partner" through the Brexit process.

"We will of course work with them as they go through the transition they are embarking upon, he told journalists during a news conference.

"We will continue to look for ways to create closer trade ties and opportunities for better jobs and economic growth that benefits both or countries."

BBC Radio 5 live

The UK could have a "super-Canada deal" with the EU, Conservative MEP David Campbell Bannerman has told BBC Radio 5 live .The Leave means Leave campaigner - a former UKIP MEP - said there had been a "change in tone" from the EU after PM Theresa May made it clear she was not looking for a special "cherry-picking" deal within the single market. "Now we want a clean break, we're not in the single market, not in the customs union, we can have a Canadian-style arrangement with the EU - that works, it's simple," he said. "Canada is a free sovereign nation, it’s got access to 99% of the EU single market, with no freedom of movement, no fee to pay and we’re not asking Canada to join the EU."

BBC News Channel

Lord Heseltine earlier gave what presenter Huw Edwards described as a "forthright" interview on the BBC News Channel.

Here are some of the main points the Conservative peer and former minister - who is a passionate supporter of EU membership - made.

• He said the Article 50 letter was full of "platitudes", trying to put a positive slant on the fact that the UK was facing an unprecedented loss of power
• The UK would soon learn the "hard way" that as good a deal as it now has would simply not be on offer during the negotiations, as this would incentivise other countries to follow the UK and try and leave
• Free trade was "just a slogan" and it was "inconceivable" that the UK would reach such an agreement with the 27 other members
• He expressed surprise that there could be any suggestion that security co-operation was negotiable as part of the Brexit talks, saying "when he first heard that he thought there must be some mistake". 
• He characterised his attitude towards Brexit as "resist and change" 

BBC News Channel

Speaking in Brussels, Danish politician Jeppe Kofod says the UK leaving the EU is like "losing a sibling", with Denmark having joined the bloc at the same time.

"It's not a day for joy - not for the UK, not for the EU, Denmark or anyone else," he adds.

Reality Check

In her interview with Andrew Neil, the prime minister said the UK would get the same benefits on trade outside the EU as inside: “It will be a different relationship, but I think it can have the same benefits in terms of that free access to trade.” 

That sounds quite similar to what Brexit Secretary David Davis told the House of Commons on 24 January – that the government was aiming for a trade and customs arrangement with the “exact same benefits” as we currently have. 

The EU’s chief Brexit negotiator, Michael Barnier, seems to disagree: he told a committee of the EuropeanParliament , external last week that by choosing to leave the single market and the Customs Union, the UK would “find itself in a less favourable situation than that of a member state”.

The full interview with Theresa May will be shown on BBC1 at 7pm.