BA said it aimed to operate the majority of services from London Heathrow on Sunday and a near normal schedule from Gatwick, the capital's second busiest airport.
However, it did not appear to be a cyber-attack, according to chairman and chief executive Alex Cruz, who said the root cause appeared to be a "power supply issue".
Travellers wait stranded at Heathrow Airport Terminal 5 after British Airways flights where cancelled at Heathrow Airport in west London on May 27, 2017.
A man who was caught up in the delays at Heathrow airport after British Airways' systems outage said the airline had lost his and dozens of other passengers' bags by the time his flight landed.
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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.
Other airlines flying in and out of the two airports were unaffected.
"We rebooked for Venice for tonight, which they also have canceled now", she told Sky News.
A spokeswoman for BA could not immediately detail the exact number of flights canceled on Saturday.
The airline has said it will refund reasonable costs to passengers, and assist them with rebooking flights.
"We were told that we would get compensation for the delay and cancellations but that we don't know how long that would take".
"We helped her up and she said "I'm just so tired".
Some British media speculated the system failure was the result of a cyberattack but British Airways rejected that claim.
Computer glitches and outages have plagued BA and other airlines in recent months.
Meanwhile, the Guardian newspaper reported here that British Airways GMB union has said the airline's decision to outsource hundreds of IT jobs to India previous year was behind the flight disruptions.
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North Korea link to NHS hacking attack
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LeEco's Jia Yueting steps down as CEO of main listed unit
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Rain washes out NCAA women's golf play
Wallace fell out of contention for the overall tournament with a 42 on his first nine holes, but Sagoo backed up as well. Penn State and Golfstat number one ranked USC were the only teams with two or more golfers in the top-10.