Dozens of services were cancelled on Sunday morning and passengers have been warned not to go to the airport without rebooking or checking their flight status.
The problem has been caused by a worldwide systems failure, believed to have been caused by a power supply issue, which caused chaos in the London terminals on Saturday.
A Heathrow spokeswoman said: “Following a worldwide British Airways’ IT system issue yesterday, delays and cancellations of British Airways flights are expected today.
“Prior to travelling to the airport, all British Airways passengers who are due to fly today should check the status of their flight.
“All passengers whose flights were cancelled yesterday should not travel to the airport today unless they have already rebooked onto another flight.”
There were more than 30 BA cancellations at Heathrow by 9am on Sunday and delays of around 30 minutes to their flights from Gatwick.
London’s Kings Cross railway station was packed with people trying to make their way north, with travellers queuing out of the doors and on to the platform for the 9am train to Edinburgh.
Those that could not get on ran to the doors of the next service at 9.30am when the platform was announced, but were met on boarding with a warning from the train guard that seats could not be guaranteed for all passengers.
BA has said it is aiming to operate a “near normal schedule” at Gatwick and the “majority of services” from Heathrow.
Experts predict the disruption could continue for several days and the airline is facing huge compensation costs after all its flights from the two airports were cancelled on Saturday.
Passengers lucky enough to be aboard one of the few flights taking off on Saturday later found their hold luggage had not made it onto the plane with them.
Terry Page, 28, from London, flew from Heathrow to Fort Worth, Texas, where he and “about 50” others were told they would have to wait until Monday before being reunited with their bags, he told the Press Association.
As IT teams tried to fix the system:
• There were chaotic scenes at Gatwick and Heathrow on Saturday as people tried to make their way overseas for the long weekend and half-term school holiday.
• All of BA’s check-in and operational systems were affected by the issue, including the airline’s customer service phone lines and rebooking function.
• The incident had a knock-on effect on BA’s operations around the world.
• BA chief executive Alex Cruz said the airline was “extremely sorry” for the “huge inconvenience” suffered by customers, especially families heading on half term holidays.
• Travellers have been told to check the airline’s website and Twitter account for updates before setting off for the airport.
BA were unable to say how many flights would be cancelled on Sunday or how long the disruption is likely to continue for.
A spokesman said: “Our focus is on updating customers and doing what we can to get them to their destinations as quickly as possible.”
The glitch is believed to have been caused by a “power supply issue” and there is no evidence of a cyber attack, the airline said.
BA initially cancelled all flights before 6pm on Saturday but later announced planes would be grounded for the rest of the day and warned passengers not to go to the airports.
Customers who saw their flights cancelled are being refunded or rebooked on to new services and other options are available for those who no longer want to fly.
The airline had issues with its online check-in systems in September and July last year, causing severe delays for passengers.
A Gatwick spokesman said: “We would advise customers travelling with British Airways over the bank holiday weekend to continue to check the status of their flight with British Airways before travelling to the airport.
“Customers affected by Saturday’s flight cancellations should not travel to the airport today unless they have already rebooked onto another flight.”