British Airways has cancelled all flights from Heathrow and Gatwick until 18:00 BST because of computer problems.
A “major IT system failure that is causing very severe disruption to our flight operations worldwide”, the airline said.
It apologised for the “global system outage” and said it was “working to resolve the the problem”.
Heathrow Airport said it was “working closely” with BA to solve the issue.
There is no evidence at this stage to suggest the system failure was caused by a cyber attack, BA told the BBC’s business correspondent, Joe Lynam.
All affected passengers will be offered the option of rescheduling or a refund.
In a statement, the airline asked passengers with flights before 18:00 BST on Saturday not to come to Gatwick or Heathrow airports, which it said had become “extremely congested”.
Other airlines flying in and out of Heathrow and Gatwick are unaffected.
The problems mean parts of BA’s website are unavailable and some travellers claimed they could not check in on the mobile app.
BA aircraft landing at Heathrow are unable to park up as outbound aircraft cannot vacate the gates, which has resulted in passengers being stuck on aircraft.
Journalist Martyn Kent said he had been sitting on a plane at Heathrow for 90 minutes. He said the captain told passengers the IT problems were “catastrophic”.
BA staff in Heathrow’s Terminal 5 were resorting to using white boards, according to passenger Gareth Wharton.
Delays have been reported in Rome, Prague, Milan, Stockholm and Malaga due to the system failure.
Philip Bloom said he had been waiting on board a Heathrow-bound flight at Belfast for two hours.
He added: “We haven’t been told very much just that there is a worldwide computer system failure.
“We were told that we couldn’t even get on other flights because they are unable to see what flights we can be moved to.”
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