Other airlines flying in and out of Heathrow and Gatwick are unaffected.
Others said they had been left stranded on the tarmac.
BA staff in Terminal 5 were resorting to using white boards, according to passenger Gareth Wharton.
BA said it would try to get affected customers onto the next available flight although the re-booking process was being hindered by the system problems.
BA has not said what is causing the computer failure.
Speaking from the plane, 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.
The system outage has affected the company's call centres and its website.
And in July, Southwest Airlines canceled more than 1,000 flights following a system failure. "There was a huge queue for it and it later transpired that it didn't actually work, but you didn't discover that until you got to the front". Passengers on social media reported long delays at check-in desks and flights being held on runways.
The disruption comes at the start of a bank holiday weekend and during half-term school holidays in the UK. "No updates or staff around", travel writer and blogger @WildWayRound tweeted.
"This could have all been avoided", Mick Rix, national officer for aviation at the GMB union, told the wire service.
While not that frequent, when airline outages do happen, the effects are widespread, high-profile and can hit travelers across the globe.
The airline has suffered other IT glitches recently, leading to severe delays for passengers in July and September a year ago. Airline officials gave no indication of what might have caused the problem or when it would be fixed.
Delta said it lost $100 million in revenue as a result of the outage. "Computer problem solved? #britishairways".
But the problem did not appear to be restricted to the United Kingdom and there were reports of flights being affected across the world.