Customers complained of "shambles" at Heathrow as a source told The Sun Online an urgent message was sent to staff warning of a "world wide system failure".
But British Airways has downplayed the problem, reportedly calling it a "temporary glitch".
Many flights were still late in departing at 10pm on Friday from several airports around the globe, including New York, Los Angeles, London, Paris and Berlin.
Most faced between an hour and two hours delay.
The majority of the complaints began appearing on Twitter in the early afternoon.
Customers complained of queues at the London airport and difficulties checking in.
The airline wouldn't give an exact number of disruptions but said some flights were delayed.
Broadcaster Andrew Neil tweeted from the scene: "Yet another computer failure at Terminal 5 Heathrow for British Airways.
"Now regular occurrence. Flights delayed. Usual shambles, not yet on huge scale.
"We're 75 minutes late. And still not taken off. Is that your idea of normal?"
3Another Passenger Derek Frome added: "'Paralysed' and 'stranded' are not the words you want to hear from your flight status update.
"The plane is ready to take off, but we're stuck waiting in the terminal because the computer system for boarding is down and there's no backup system."
British Airways has been contacted by The Sun Online for comment.
But the company told the Daily Mail there was: "A temporary glitch with some of our internal systems has been resolved.
"Our customers have continued to check in and fly to their destinations as normal."
Earlier the airline had posted a tweet saying: "We are working to resolve a technical issue with some of our internal systems, including our call centres.
"Flights are continuing to operate and customers are able to check in as normal."
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