Thousands of holidaymakers were stranded after British Airways suffered a global IT crash, grounding scores of planes.
The major system failure, believed to have been caused by a power supply issue, has affected operations around the world.
Experts predict the disruption could continue for several days and the airline is facing huge compensation costs after all BA flights from Gatwick and Heathrow were cancelled on Saturday.
There were chaotic scenes at the London terminals as people tried to make their way overseas for the long weekend and half-term school holiday.
BA initially cancelled all flights before 6pm on Saturday but later announced that planes would be grounded for the rest of the day and warned passengers not to go to the airports.
It is feared that it could take days for services to return to normal and clear the backlog of passengers.
Air industry consultant John Strickland said the disruption could "run into several days" and added: "There's a massive knock-on effect.
"Customers and from the airline's point of view - manpower, dealing with the backlog of aircraft out of position, parking spaces for the aircraft - it's a challenge and a choreographic nightmare."
Several travellers at Heathrow told the Press Association they were not told their flights were cancelled until more than an hour after the airline put out a press statement announcing the decision.
Student Emily Wilson told the Press Association: "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."
At Gatwick frustrated passengers could be seen surrounding BA staff at the check-in as they handed out letters which apologised for the cancellations and gave details about how to claim for hotels, local transport and refreshments.
Teacher Gemma Richardson, 30, who is 24 weeks pregnant, said "it was chaos" when she and her husband arrived at the airport with their two-year-old daughter.
"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," she added.
BA has apologised for the disruption and says IT teams are "working tirelessly" to fix the problem.
Chief executive Alex Cruz said: "We are extremely sorry for the huge inconvenience this is causing our customers and we understand how frustrating this must be, especially for families hoping to get away on holiday."