A massive IT systems failure led to all flights from Heathrow and Gatwick being cancelled on Saturday.
British Airways says it is aiming to run a “near normal schedule” at Gatwick and the “majority of services” from Heathrow on Sunday after IT failure led to all flights being cancelled.
Serious problems with BA’s systems led to thousands of passengers having their plans disrupted on Saturday.
Passengers described “chaotic” scenes at the airports, with some criticising BA for a lack of information.
The airline apologised and said it was refunding and rebooking customers.
BA advised customers to continue checking the status of their flight on its website www.ba.com before travelling to the airport.
The airline said there was no evidence the computer problems were the result of a cyber attack.
The company’s chief executive Alex Cruz had said it was believed “the root cause was a power supply issue”.
Other airlines flying in and out of the two airports were unaffected.
BA said although some of its IT systems have returned, “there will be some knock-on disruption to our schedules as aircraft and crews are out of position around the world.
“We are repositioning some aircraft during the night to enable us to operate as much of our schedule as possible throughout Sunday.”
A BA spokesman added: “We are continuing to work hard to restore all of our IT systems…
“We are extremely sorry for the huge disruption caused to customers throughout Saturday and understand how frustrating their experiences will have been.
“We are refunding or rebooking customers who suffered cancellations on to new services as quickly as possible and have also introduced more flexible rebooking policies for anyone due to travel on Sunday and Monday who no longer wishes to fly to/from Heathrow or Gatwick.”
Earlier, the airline said most long-haul flights due to land in London on Sunday were expected to arrive as normal.
The GMB union had suggested the failure could have been avoided, had the airline not outsourced its IT work.
BA denied the claim, saying: “We would never compromise the integrity and security of our IT systems”.
Aviation expert Julian Bray told the BBC the problem froze the entire system impacting on planes taking off, as well as baggage, and accessing passenger details.
“This is a very serious problem, they should have been able to switch to an alternative system – surely British Airways should be able to do this, ” he said.
BA aircraft landing at Heathrow had been unable to park as outbound aircraft could not vacate the gates, which resulted in passengers being stuck on aircraft.
Delays were also reported in Rome, Prague, Milan, Stockholm and Malaga due to the system failure, which coincided with the first weekend of the half-term holiday for many people in the UK.
Some passengers reported having to leave Heathrow without their luggage on Saturday.
BA confirmed the IT failure had led to a “significant number” of bags being left at the airport. It urged passengers not to return to collect their luggage, saying it would be returned to them via courier free of charge.