British Airways has cancelled all flights from Gatwick and Heathrow for the rest of Saturday after a global IT crash.
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."
Scores of Britons were stranded as they tried to fly overseas for the long weekend and half-term school holidays, with many venting their frustration on BA's twitter page.
Several passengers at Heathrow told the Press Association they had not been told their flights were cancelled until more than an hour after the airline put out a press statement announcing the decision.
Images posted online showed a group of people gathered around the customer services desk at Terminal 5 trying to get information.
Terry Page, 28, from London, said: "There's no such announcement here. The boards are showing 'Go to gate' and no mention of cancellations."
More than an hour later, he said cancellations of individual flights were still being announced.
Footage filmed at the terminal showed long queues at customer services, after passengers had been advised that they would be unable to rebook due to systems remaining down.
Student Emily Wilson told the Press Association that she had been advised "we are unable to get bags, and that no more flights are taking off", several hours after having arrived at the airport for her flight to Stockholm.
Ms Wilson added: "We were told (it would be) about three hours for collecting bags, that all compensation will have to be done online, and that we are unable to rebook flights now because of the system being down."
She said that information on screens still suggested her flight could board shortly, but that staff contradicted that information, saying there were "no slots left".
Dan Power said he and his 80-year-old grandmother are stranded at Heathrow, waiting for a flight to Milan, and have had no information from BA.
He told BBC News they have been offered "absolutely nothing" in the way of refreshments and added: "We haven't been offered any chairs, any water, any vouchers - nothing.
"I don't think our week's holiday will happen at this rate.
"My main concern now is I don't want my 80-year-old grandma spending the night on Heathrow floor - but all the hotels are fully booked, we don't have any transport back up north, so we are actually stuck in Heathrow with nowhere to go."
Travellers have been told to check the airline's website and Twitter account for updates on the situation.
The airline has experienced issues with its online check-in systems in the past.
Passengers were hit by severe delays in September and July last year because of IT glitches.
Frustrated passengers could be seen calmly surrounding BA staff at the check-in at Gatwick airport.
BA staff were handing out letters which apologised for the cancellations and gave details about how to claim for hotels, local transport and refreshments.
Bernadette Young, 38, from Farnham, Surrey, was travelling to Portugal with her husband Cris, 37, and daughters Beatrix, five, and Theodora, two, for their first family holiday in three years.
Mrs Young, who had been a teacher before becoming a stay-at-home mother, said: "We cannot get on a flight today and we have been offered a flight from Manchester tomorrow but we cannot drive up there.
"The girls are really disappointed. It is half-term and we have only got a week. They were looking forward to it and really getting excited about going swimming in the sun.
"Hopefully we will still be able to go."
Mrs Young said "it doesn't help to be hysterical about an unfortunate situation", adding: "Given what has happened this week in Manchester, this is not the worst thing in the world.
"I also think that if BA were not offering compensation, I might not be thinking that way. I think a lot of people are just giving up and cancelling."
Teacher Gemma Richardson, 30, who is 24 weeks pregnant, was travelling with her husband David, 30, and their two-year-old daughter to Spain.
Mrs Richardson, who was sitting uncomfortably on a barrier, said "it was chaos" when they arrived at the airport.
She said: "There was no formal guidance, just information on a screen saying that the flights up to 6pm had been cancelled.
"We all pooled around a BA employee who was doing her best to give advice.
"It seems that because it is a bank holiday weekend there is no spare flights. We are on standby but it is very unlikely we are going anywhere.
"It is all stressful but we are trying to put a best face on it for my daughter but it is very difficult.
"There are no real chairs here so I am sitting on a barrier which is not great."
Linda Murakami, 55, had flown in from her home in Pennsylvania, US, for a connecting flight to Naples, Italy, only to find it had been cancelled.
She is now cancelling a "dream holiday" to the Amalfi coast with her family.
Miss Murakami, who retired early from a pharmaceutical company, said: "This trip was my retirement present.
"There are a lot of other things that can cause disappointment and could put everyone in a worse situation.
"We just have to be flexible. We have travel insurance so feel that because we would miss part of the vacation, we might as cancel it and just go again at a different time. For me, it is an inconvenience."
Her friend Joyce Cohen, of New Jersey, said: "This had been my dream vacation. Everything had been worked out so that I could come. I am very upset.
"I have waited for this my whole life and I am not in good health, so who knows what could happen by next year when I could come again."