British Airways has grounded all flights from Heathrow and Gatwick on Saturday because of a "major IT system failure".
Passengers have been told to check before travelling to airports as the computer crash affected flights worldwide.
But the airline said: "We have found no evidence that it's a cyber attack."
Travellers have been advised to check the airline's website and Twitter account for updates about the situation.
BA first said it would affect flights up until 6pm but it has now cancelled all flights leaving from Gatwick and Heathrow for the rest of today.
However, BA's website is currently unavailable and some travellers have said they were unable to check in on the mobile app.
Passengers have been told not to travel to the London airports because of "extreme congestion", with scores left stranded at the terminals.
A spokeswoman for the airline said: "We are working hard to get our customers who were due to fly today onto the next available flights over the course of the rest of the weekend. Those unable to fly will be offered a full refund."
BA said delays could continue into Sunday, but most long-haul flights should be able to land as normal in London.
"Following the major IT system failure experienced earlier today, with regret we have had to cancel all flights leaving from Heathrow and Gatwick for the rest of today, Saturday, May 27," the statement added.
"The system outage has also affected our call centres and our website but we will update customers as soon as we are able to.
"We are extremely sorry for the inconvenience this is causing our customers during this busy holiday period."
ITV News Royal Editor Chris Ship is among hundreds of passengers caught up in the disruption at Heathrow Airport.
Former Fun House presenter Pat Sharp said he was stranded on the tarmac in Oslo.
He tweeted: "Hey British Airways we are stuck on in your plane on the tarmac in Oslo and need to get to Heathrow Airport so please can you update us?"
Many people took to social media to vent their frustration.
One passenger, Henry Tail, tweeted he missed his flight as a result.
Another, Philip Bloom, posted: "Stuck on a @British_Airways plane at Belfast going nowhere. “BA computers down worldwide” whatever that means! #britishairways"
Gareth Wharton, who is at Heathrow Terminal 5, tweeted a picture of BA staff writing gate information on a whiteboard amid the systems outage.
"Gets worse, #T5 staff having to put gate info up on a white board #LowFi #Heathrow," he wrote.
Julie Adie wrote: "We are on the runway.. For hour now..no offer of drinks..and because ba only takes cards now, we only have cash...wat we supposed to do!!?? (SIC)"
BA has previously experienced problems with its online check-in systems
Passengers were hit by severe delays in September and July last year because of IT glitches.
The airline's problems come a day after passengers at Gatwick Airport faced long queues due to a baggage system problem.
Those taking flights on Friday were forced to travel without their hold bags and were asked to carry any essential items in their hand luggage.