An updated statement from British Airways now. Here's what they're saying:

British Airways is advising its passengers on short-haul flights:

• Not to travel to the airport unless their flight is shown to be operating
• Any customers due to travel today or tomorrow can move their flights free of charge to a later date, subject to availability
• Any customers who have had their flight cancelled are being rebooked on other BA flights and alternative carriers

A reminder that if your flight is cancelled, you may be entitled to compensation.

Here's a handy graphic to see whether you qualify. You can read our full explainer here.

Rob Corp
Live reporter

Image source, Reuters

Nats' announcement at 15:15 BST that the problem with its air traffic planning system had been resolved means that airliners and their passengers should begin moving again - but there will still be disruption until the end of the day.

There are several reasons for that - not least getting delayed flights refuelled and their fare-paying customers on board - but also that some of the crews will have run out of hours in the meantime.

Fatigue is a big concern in aviation, so the hours pilots and cabin crew work are strictly regulated. And if that crew's hours expired while waiting on the ground, then the airline will need to find replacements to take over their flight.

Also, there are now a whole load of airliners parked up at airports around the country taking up gate space. The airlines will need to get them away so the delayed flights waiting to get back to the UK can take off and make their way home. It's all a big logistical puzzle and it will take several hours for all the pieces to be put back into place.

Kris's original flight from Palma in Mallorca on Saturday was delayed - he’s now looking at a flight more than 24 hours later.

"We have been stuck in Palma airport since 7pm yesterday, with little to no information on how we are getting home through Jet2," he told the BBC.

"Our first flight was pushed back from 10pm to 2am. Then 4am. And then it just got cancelled."

He said they've been lying on the airport floor along with hundreds of people.

He adds that the airline "haven’t provided adequate food or water vouchers," and several families - especially those with young children - are struggling.

"I’ve never experienced a worse service in my life."

Transport Secretary Mark Harper says the "technical issue" affecting National Air Traffic Services "has now been resolved".

In a post on X, formerly known as Twitter, he says he is continuing to work with Nats to "help them manage affected flights and support passengers" alongside Aviation Minister Baroness Vere.

"All passengers should still contact their airline for specific flight information," Harper's latest statement says.

Image source, PA Media

British Airways has said it will make "significant changes to its schedule" after UK air traffic control suffered a significant technical fault.

Posting on X, external (formerly Twitter), BA urged passengers travelling on a short haul service today, not to travel to the airport "without checking the status of your flight, as it may no longer be operating."

"You can do this by visiting www.ba.com/managemybooking and checking your email inbox," the post adds.

So, the issue's been fixed - but the question now is how bad the knock-on delays will be for those caught up in today's disruption. Here's a look at the latest developments on this story:

• In the last few moments, UK air traffic control service Nats declared that it had "identified and remedied the technical issue"
• It apologised for the disruption caused by the fault and said it was "working closely with airlines and airports" to get things running as normal again
• Nats said the issue had been with its planning system, meaning that flight plans had to be processed manually
• Transport Secretary Mark Harper said in the last hour his team was doing "all we can" to support Nats
• More than 500 flights into and out of the UK have been cancelled as of 14:30, according to aviation analytics firm Cirium
• Airlines and airports across the UK have issued warnings of delays - making the point that these were out of their control and advising travellers to check their flight is operating before leaving for their airport
• Passengers have spoken to the BBC about hours spent waiting on airport tarmac

An 18-year-old woman from Londonderry said she and other passengers are currently stuck on an aircraft at Alicante Airport as a result of issues affecting UK air traffic control.

“We were being told as we were boarding that it may not be until 10:30 tonight until we could get going, but we’ve been kept on the flight just in case we were told that we can fly any earlier.

“We boarded the [Jet2] flight at 11:40 today and have been sat here ever since.

“They’ve given us water, but if you want any food or soft drinks, or anything like that you need to pay for it.”

Ms McGregor-King said everyone on the plane is starting to get “very frustrated” and is eagerly awaiting an update about when or if they will be able to fly.

The Derry woman was in Spain with her family, but said they are set to travel from Alicante on a separate flight later today.

“I don’t know if my mum’s flight will be cancelled and they’re stuck out here or my flight will be cancelled and they can travel – I just don’t know.”

Image source, Ebonie McGregor-King

Here's that latest statement in full from National Air Traffic Services (Nats):

"We have identified and remedied the technical issue," UK air traffic control service Nats has said in a fresh statement.

We'll bring you more on this shortly.

In the last few minutes, we've had a comment from Transport Secretary Mark Harper.

He's posted, external to say that airspace remains open but traffic flow restrictions are in place.

Harper adds that he and his ministerial colleague Charlotte Vere are doing "all we can to support" National Air Traffic Services (Nats) as it works "at pace" to fix the issue.

"In the meantime, passengers should contact their airline for up to date flight information."

Alastair Rosenschein, a former pilot and aviation consultant, tells BBC Radio 5 Live that what is happening at UK air traffic control is equivalent to what it would be like on the ground "if every road was closed."

And the delay could last even longer than the technical issues. There are restrictions on how many hours crews can work; “so if a delay is particularly long they will go out of hours before they even take off,” he says.

Some operations should still be able to carry on, Rosenschein says, “if you reduce the traffic flow by a great deal".

"While this doesn’t happen very often, preparations are in place and the organisation is there to manage this sort of situation.”

Data from aviation analytics firm Cirium as of 14:30 BST revealed that hundreds of flights had been cancelled today.

• 232 flights departing UK airports have been cancelled - equivalent to 8% of all departures
• 271 flights arriving at UK airports have been cancelled - equivalent to 9% of all arrivals

The agency points out that this data only reflects cancelled flights, and not delayed ones. Several flights have currently been delayed by more than eight hours, which will "inevitably" lead to a cancellation.

Cirium adds that the data is likely to change as the day goes on.

Here's a quick look at what we've heard so far from airlines which operate in the UK.

• Jet2 gives a sense of the scale of the issue - saying the fault has affected "all airlines", and that "all flights departing and returning to the UK are expected to experience significant delays"
• British Airways and Wizz Air have both said they're "working closely" with National Air Traffic Services to get to grips with the issue and keep passengers informed
• Ryanair has joined other airlines in issuing an apology to affected passengers, and makes it clear "the ATC (air traffic control) failure... is beyond Ryanair's control"
• Aer Lingus makes the same point, and says the issue has meant "severe restrictions on all flights into the UK and flying over UK airspace today"
• Tui has issued this advice to its customers: "Monitor the departure boards or your emails for further updates". Virgin Atlantic has a similar message; its passengers have been urged to check their flight status in advance on the airline's website
• Scottish provider Loganair raised the alarm earlier, reporting a "network-wide failure of UK air traffic control systems this morning"

And if you are affected - here's more on what you can expect from your airline.

Darran Marshall
Reporting from Belfast International Airport

EasyJet has just confirmed a significant number of cancellations at Belfast International Airport.

The departure board is currently showing cancellations - to destinations including Faro, Newcastle, Birmingham, and Amsterdam.

The Liberal Democrats are weighing in now on the response to today's air traffic control issues.

The party is calling on Prime Minister Rishi Sunak to convene a Cobra emergency meeting and "get a grip on this issue urgently".

"Millions of holidaymakers could be facing huge disruption in the coming days due to this fault and we can't risk this government being missing in action yet again," transport spokesperson Wera Hobhouse says in a statement.

She says the UK needs to know that the government is doing "all it can to make sure people aren't hit with major delays and disruptions in the coming days".

Image source, Press Association

The Labour Party's shadow transport secretary Louise Haigh says today's flight delays in the UK are "extremely concerning for passengers".

In a post on X, external (formerly Twitter) she says the UK's airspace "is not closed but significant delays expected thanks to a technical fault."

Haigh adds that she is "surprised" Transport Secretary Mark Harper has not made a statement.

We have a fresh statement from Nats which says the technical issue is affecting the organisation's ability to automatically process flight plans - the information air traffic controllers need to know about where an aircraft is flying from and at what time, along with where it's going and the route it will take to get there.

"Until our engineers have resolved this, flight plans are being input manually which means we cannot process them at the same volume, hence we have applied traffic flow restrictions," a spokesperson says.

"Our technical experts are looking at all possible solutions to rectify this as quickly as possible.

Nats reiterates the top priority is ensuring every flight in the UK remains safe as it advises any passengers travelling to contact their airline.

Catherine Wyatt
BBC News

I’m at Luxembourg airport where my flight to London Stansted has been cancelled.

Ryanair emailed us the news - there’s no information at the gate, where we are still waiting for someone to help us retrieve our checked baggage and leave the airport.

Passengers are quite stressed and are on their phones trying to rebook new flights as there are no airline staff around. We couldn’t find any direct flights today on any airline.

So we rebooked on the next available Ryanair flight which is tomorrow afternoon. It was good I rebooked straight away - other passengers are now finding out about the cancellation and realising there’s no Ryanair flight back until Thursday.

As there’s no information at the airport, only via email or the Ryanair website, I think there are some passengers here who aren’t actually aware the flight has been cancelled.

Image source, Getty Images

A fresh statement to bring you from Wizz Air - the Hungarian-based airline which is one of the UK's largest low-cost airlines operating mainly from Luton and Gatwick.

A spokesperson for the airline acknowledges that "heavy delays" and cancellations are possible today due to the UK-wide air traffic issue.

Wizz Air says: "We are working closely with the National Air Traffic Services to do everything possible to minimize the impact this will have on our passengers."

Customers who booked directly with Wizz Air will be contacted by email or text to keep them up to date on the developing situation and offering alternative flights or refunds, the airline adds.