Holidaymakers have been hit by bank holiday travel delays after a UK air traffic control failure meant flight plans had to be input manually by controllers.

National Air Traffic Services (Nats), the country’s leading provider of air traffic control, said at 3.15pm that it had “identified and remedied” the technical issue affecting its systems and it was working with airlines and airports to support affected flights.

Major UK airlines such as Tui and BA have warned of “significant delays” for passengers amid changes to schedules.

The Nats statement added: “We are now working closely with airlines and airports to manage the flights affected as efficiently as possible.

“Our engineers will be carefully monitoring the system’s performance as we return to normal operations.

“The flight planning issue affected the system’s ability to automatically process flight plans, meaning that flight plans had to be processed manually which cannot be done at the same volume, hence the requirement for traffic flow restrictions.

“Our priority is always to ensure that every flight in the UK remains safe and we are sincerely sorry for the disruption this is causing. Please contact your airline for information on how this may affect your flight.”

Flights will remain “significantly disrupted” for the rest of Monday, despite the technical issue being resolved, a spokesman for Heathrow Airport said.

British Airways told passengers on Monday that no flights would take off until 6pm and all check-in desks were closed.

Lawrence Sinclair, 26, who works for a holiday company, told the PA news agency he had to book on to a new BA flight to Gothenburg in Sweden, which leaves at 8.50pm, after his earlier flight was cancelled.

He said: “I don’t know if the later flight is going to go or not. I was supposed to go at 3.50pm.

“Hopefully I will fly at 8.50pm but that is going to be delayed, isn’t it. It’s annoying, I’m going to see my girlfriend in Sweden, but if I don’t go today I’ll go tomorrow.”

Irene Franklin, 60, had her Delta flight from Heathrow to Austin, Texas – with her daughter, son-in-law and two friends – cancelled at the last minute.

She told PA outside Terminal 3: “It was (saying delayed by) two hours, now it’s cancelled. It’s now not until tomorrow morning at 10.

“It’s frustrating but what are you going to do?”

Asked if she had been offered compensation, she said: “No. Not for a place to stay tonight, not for a cab ride.

“The Delta customer service was really helpful, he got us on to the same flight with seats together but he didn’t really do anything else.

“We have a hotel booked but we have to pay for it and our meals.”

Daniela Walther, 44, was supposed to leave Heathrow for Stuttgart, Germany, on a BA flight at 5.25pm but it will now leave later than 1am.

She said staff had been helpful but it “took a while to find someone to talk to”.

She added: “I know it’s going to be long but on the other hand I don’t dare to leave because I don’t want to miss information, and I don’t know if I don’t get it on my phone.”

A retired barrister who is stuck in Sardinia claimed an easyJet pilot said he had not seen an incident like this in 20 years.

Gemma Saleh, 43, who teaches part-time at law school and lives in Newcastle, told PA she boarded an easyJet flight with her family at 11.30am Sardinia time (10.30am London time), which was heading for Gatwick, and she remained on the plane for close to two hours.

She said: “We were told as we started to taxi there was an issue with the air traffic computer but he didn’t know more and we’d wait on the tarmac till we got a slot.

“[The pilot] also said as we are ‘rescue’ we would be able to find a slot soon, maybe 30 mins.

“He’s not seen this in 20 years.”

Mrs Saleh, with her husband, a 43-year-old surgeon, and their two children, aged 10 and eight, and other passengers on the flight, were taken by bus back to the terminal to “wait it out there”.

She said easyJet provided free snacks and she is not sure when she will return home, with that flight having already been delayed since Sunday.

On Monday, 3,049 flights were due to depart UK airports and 3,054 were scheduled to arrive, according to analysis by aviation analytics firm Cirium.

This equates to more than 540,000 seats on departing planes and 543,000 on arriving planes.

Ryanair passengers waiting at Stansted Airport in Essex said there were cheers when two flights to Copenhagen and Paphos were announced for boarding.

They said they had heard airlines cancel about five flights while they had been waiting at the gate.

A passenger at Stansted said: “After boarding the flight we’ve been sitting on the tarmac ever since. Pilot said we boarded so could get in the queue to have our flight plan manually processed.

“He’s now come back on to tell us the system is fixed but there’s still lots of delays.

“We’ve been given a take-off slot for one hour’s time. By that time flight will be over four hours late taking off.”

Transport Secretary Mark Harper said ministers were working with Nats to “help them manage affected flights and support passengers”.

He tweeted: “The technical issue affecting @NATS has now been resolved.

“Aviation Minister @CharlotteV and I are continuing to work with NATS to help them manage affected flights and support passengers.

“All passengers should still contact their airline for specific flight information.”

Home Secretary Suella Braverman sympathised with anyone affected by the problems.

She told broadcasters on Monday: “I am very cognisant that this will disrupt people’s travel plans – those who are waiting to arrive in the UK, those waiting to depart, and I do sympathise with any disruption they may be experiencing.”