Cruz, the chief executive, said a power supply problem is believed to have triggered the crisis.
Outbound passengers who haven't arrived at the airport yet are being asked to stay away until there is confirmation that flights have resumed.
It said it expected that London-bound long-haul flights would land on schedule Sunday. With the IT system failure, British Airways staff ultimately had to resort to white boards to write gate numbers.
"We've tried all of the self-check-in machines".
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Terry Page, 28-year-old man from London, who was flying on a BA to Texas, was trapped in a queue in Terminal 5 for two hours.
Speaking from the plane, Miss Davis said the air conditioning had been off "so I don't think we will be going anywhere any time soon", but added that the passengers had been kept informed by their pilot and given water while they remained seated.
British Airways said there was no evidence that a global breakdown of its IT systems had been caused by a cyber attack.
The airline apologised and said it was refunding and rebooking customers.
The problems, which passengers said had affected flights across Britain, came on a particularly busy weekend with a public holiday tomorrow and many children starting their school half-term breaks.
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He has, however, indicated that his future will be discussed at a club board meeting after the FA Cup Final. "I've turned down every club in the world to stay here".
BA has not said what is causing the computer problem, but says it is working to resolve it as quickly as possible.
It's not the first time computer problems have caused hassles at BA.
The airline said in response that it would "never compromise the integrity and security of our IT systems", adding that outsourcing of IT services was a "very common practice across all industries". In January it suffered another glitch that grounded flights in the U.S. That same month, United also grounded flights because of a computer problem.
BA denied the claim, saying: "We would never compromise the integrity and security of our IT systems". "There's just hundreds and thousands of people accumulating in the departures bit".
There are "thousands of people there with no idea where their bags are or what to do", she said.
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