Casa Arabe is committed to being a meeting point between Spain and the Arab world
The carrier apologised for the "current IT systems outage".
"We are working to resolve the problem as quickly as possible," it said in a tweet.
Heathrow Airport said it was "working closely" with BA to resolve the issue.
There is no evidence at this stage to suggest the system failure was caused by a cyber attack, British Airways told BBC.
The IT system failure came as many Britons headed overseas for the long weekend and half-term school holidays.
British Airways' website was unavailable and some travellers claimed they could not check in on the mobile app, with many venting their frustration on the social media, the Guardian reported.
Others said they had been delayed at the airport or on runways before take off.
There were reports that hundreds of bags were left unattended as BA staff tried to control the situation.
One passenger tweeted: "Stuck on a British Airways plane at Belfast, going nowhere. 'BA computers down worldwide', whatever that means!"
Another posted: "British airways computers down T5 and standstill, stranded on the plane and they make us pay for food!! Please retweet this indecency!"
A passenger claimed that BA "made no announcements at all" about the delays.
It came a day after passengers at Gatwick airport faced chaotic scenes and long queues due to a baggage system problem, said the Guardian report.
Those taking flights on Friday were forced to travel without their hold bags and were asked to carry any essential items in their hand luggage.
Casa Arabe is committed to being a meeting point between Spain and the Arab world
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