More than a third of British Airways flights from Heathrow were cancelled as thousands of passengers faced a second day of disruption.
The airline was hit by a worldwide computer system power failure on Saturday, causing cancellations and delays for thousands of passengers.
All long-haul services left from Heathrow, but with delays, BA said.
The airline has urged people to check the status of flights before travelling to the airport.
The airline apologised to customers for the issue, which is thought to have been caused by a problem with the IT system’s power supply.
In a statement released on Sunday, chief executive Alex Cruz said: “I know this has been a horrible time for customers. We’re not there yet, but we are doing our very best to sort things out for you.”
The BBC’s Phillip Norton, who has been stranded at Rome airport since Saturday, has been told he won’t be able to fly back to London until Tuesday.
The airline is liable to reimburse thousands of passengers for refreshments and hotel costs.
Customers displaced by flight cancellations can claim up to £200 a day for a room (based on two people sharing), £50 for transport between the hotel and airport, and £25 a day per adult for meals and refreshments.
One traveller from Seattle said she had spent the evening sleeping on the floor of a hotel conference room.
Ashley Tracey, who was trying to get to Mumbai for her friend’s wedding, said she had been queuing to rebook her flight for six hours.
She said: “There’s no information I can’t seem to get through online, I don’t live here so I don’t have a phone that works here.”