The incident on Bank Holiday Monday meant flight plans had to be uploaded to systems manually, slowing or cancelling air traffic across the country.

Thousands of passengers were affected by yesterday's disruption - and many are still waiting for their flights today.

Read more: Britons sleeping on floors in airports - live updates

Some 790 departures and 785 arrivals at UK airports were cancelled on Monday, according to aviation analytics firm Cirium - amounting to one third of all scheduled flights in and out of the country.

Around 281 flights were cancelled on Tuesday, including more than 70 at both London Gatwick and London Heathrow.

Ryanair chief Michael O'Leary criticised the UK NATS in a video posted on X, formerly known as Twitter, on Tuesday afternoon, saying it was "not acceptable" the system had gone down without a backup.

He said: "We still haven't had an explanation from them [about] what exactly caused this failure, and where were their backup systems?

"It's simply not acceptable that UK NATS would allow their systems to be taken down and everybody's flights get cancelled."

Mr O'Leary added his airline cancelled 250 flights on Monday, and another 70 would be scrapped until the end of the day on Tuesday.

In a statement, NATS apologised for the technical issues on Monday, saying: "We know a great many people have had their travel plans disrupted and are facing the impact of delays and cancellations.

The organisation added it was now operating normally, and an investigation was underway to work out what went wrong.

There had been speculation an "incorrectly filed" flight plan could have been behind the problem, but NATs refused to comment on the rumour, while prime minister's official spokesperson did not rule out the possibility.

Transport Secretary Mark Harper stressed technical experts have ruled out a cybersecurity incident, with the Civil Aviation Authority (CAA) set to investigate.

"Something on this scale hasn't happened for almost a decade - normally the system works very well," he told Sky News.

Prime Minister Rishi Sunak said Mr Harper would remind airlines about their responsibilities to passengers hit by air traffic control disruption, telling reporters: "I know people will be enormously frustrated by the disruption that's impacting them.

"The transport secretary is in constant dialogue with all the industry participants, he will be talking to airlines specifically later today and making sure that they support passengers to get home as quickly as possible."

Flights are running - but there are warnings of cancellations and delays

There have been reports of heated scenes at airports across Europe, with "fists flying" in Palma as exasperated tourists struggle to return home, while others sleep out in airports in the hope of catching a new flight.

Heathrow Airport says services will remain disrupted today - and passengers are being urged to contact their airline before heading to the terminal.

At least 32 departure flights and 31 arrivals have been cancelled at the west London airport.

Elsewhere, London Gatwick said it plans to operate a normal schedule on Tuesday following the disruption, though at least 23 departures and 51 arrivals were listed as cancelled at the airport.

Outside of London, most airports appear to be returning to a normal schedule, with Glasgow saying a handful of flights will be disrupted as a result of Monday's incident, while departure boards at Manchester and Bristol airports show a small number of services have been cancelled.

'I don't like the ending to this story'

Travellers from the UK have reported disruption both in the UK and abroad - with some saying they may not be able to fly until the weekend.

TV host Ore Oduba posted on Instagram saying his cancelled easyJet flight from Greece left them "stranded" with no supplies for their two toddlers, mocking the voucher they had been offered from the airline.

Meanwhile, athletes and broadcasters who have been out at the World Athletics Championships in Budapest, Hungary, have also reported delays, with sport presenter Jeanette Kwakye writing on X, formerly known as Twitter: "No idea when I'll be back, any suggestions for ways home that don't involve 36 hours of travelling or endangering my life are welcome."

She added: "I don't like the ending to this story."