British Airways has said it is aiming to operate a "near normal schedule" at Gatwick and the "majority of services" from Heathrow on Sunday after a global IT crash crippled the airline.
Thousands of passengers were stranded on Saturday after scores of planes were grounded by the major systems failure believed to have been caused by a power supply issue.
The airline said it was "extremely sorry" for the "huge disruption" it cause and that its engineers were continuing to work hard to restore its services.
Customers who saw their flights cancelled are being refunded or rebooked onto new services "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 airports on Sunday and Monday.
There were chaotic scenes at Gatwick and Heathrow on Saturday and passengers were advised to continue checking the status of their flight online after the incident affected operations around the world.
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 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.
"We would advise customers travelling across the Bank Holiday weekend to continue checking the status of their flight on our website, www.ba.com before coming to the airport."