British Airways plans to operate a “near normal schedule” from Gatwick and the majority of services from Heathrow from Sunday following a major IT system failure.
The airline cancelled all flights from both London airports on Saturday after a “global systems outage” blamed on a power supply issue.
The issue affected all of BA’s check-in and operational systems, including customer services phone lines and the facility used for re-booking flights.
The problems also created a knock-on effect on BA's operations around the world.
British Airways said it was repositioning some aircraft during the night to enable it to operate as much of its schedule as possible on Sunday.
It also warned passengers not to come to the airport unless you have a confirmed booking for travel.
The airline said any passenger booked to fly Sunday or Monday and no longer wish to travel can rebook to travel up to and including June 10.
In a statement British Airways said: “We are extremely sorry for the significant levels of disruption caused to customers and understand how frustrating their experiences have been.
“Affected customers can claim a full refund or rebook to a future date for travel up until the end of November 2017. Customers are urged to keep any food, transport or accommodation receipts and can make a claim in due course through our Customer Relations teams. There are a significant number of bags at Heathrow which we will be reuniting with customers via couriers as soon as we can. This will be done free of charge.
“Please don’t come to Heathrow to collect your delayed bags, as they are in the process of being sorted for onward distribution in secure airside locations.”
BA chairman and CEO Alex Cruz apologised to passengers in a video message.
The airline said there was no evidence the computer problems were the result of a cyber attack.
Other airlines flying in and out of the two airports were unaffected.