"Our system issue is now resolved, we are operating normally and working as hard as possible to clear the backlog of flights," air traffic control operator NATS has said.
Passengers travelling to and from the UK on Tuesday faced severe disruption after a technical glitch affected air traffic control systems.
More than 1,000 flights have been cancelled so far, according to flight-tracking website Flightradar24, with the issue impacting airports including London Heathrow, London Gatwick, Manchester, and Birmingham.
Air traffic control operator NATS said earlier that it had identified a "technical issue" with its flight processing system and that its engineers were on site and working on a solution.
"Our system issue is now resolved, we are operating normally and working as hard as possible to clear the backlog of flights," NATS later said in a post on social media, while also apologising for the disruption.
The incident has also hit flights at London Luton, London Stansted, Liverpool, and Edinburgh airports, as well as Dublin airport in Ireland, among others.
Flight disruptions are likely to continue throughout the rest of Tuesday, airports say.
In a statement on Tuesday evening, Manchester airport said it expected a full flight schedule to operate on Wednesday but warned that the airport may be busier than usual as flights were rescheduled.
Airports are advising passengers to check with their airlines before travelling.
Writing on X, British Transport Secretary Heidi Alexander said she was "pleased" NATS had remedied the problem and thanked all those "working to get people moving."
"It will take time to fully resume flights, so continue to check with airlines," she wrote, adding: "I am seeking assurances that lessons will be learned and systems that support aviation are up to the job."