Customers whose flights were cancelled are being refunded or re-booked "as quickly as possible"
British Airways says it is "aiming to operate a near-normal schedule" after an IT failure hit thousands of passengers.
All flights were cancelled from London's Heathrow and Gatwick airports on Saturday due to what was described as a "global systems outage" blamed on a power supply issue.
Thousands of passengers were left stranded and terminals at both airports were "extremely congested", with travellers urged to stay away.
All of BA's check-in and operational systems were affected, including customer services phones lines and the facility used for re-booking flights.
The problems also created a knock-on effect on BA's operations around the world.
At this stage we're aiming to operate a near normal schedule of flights from Gatwick and the majority of our Heathrow services on Sunday.3/5— British Airways (@British_Airways) May 28, 2017
A BA spokesman said: "We are continuing to work hard to restore all of our IT systems and are aiming to operating a near normal schedule at Gatwick and the majority of services from Heathrow on Sunday.
"We are extremely sorry for the huge disruption caused to customers throughout Saturday and understand how frustrating their experiences will have been.
"We would advise customers travelling across the Bank Holiday weekend to continue checking the status of their flight on our website, before coming to the airport."
Please don't come to the airport unless you have a confirmed booking for travel. 4/5— British Airways (@British_Airways) May 28, 2017
It is possible the disruption may last several days, however, as planes and aircrew are returned to their positions and the backlog of passengers is cleared.
Customers who had their flights cancelled are being refunded or re-booked "as quickly as possible" and more flexible booking policies are being put in place for those who no longer want to fly to or from the airport on Sunday and Monday.