Reports claim the airline has been victim of a cyber attack, although BA has denied there is any evidence of this.
The outage comes as scores of Britons are headed overseas for the long weekend and half-term school holidays on Saturday morning.
BA has now confirmed all flights from Heathrow and Gatwick will be cancelled until at least 6pm today.
A spokeswoman for the airline said: “We apologise to customers who are facing some delays following an IT outage this morning. We are working to resolve the problem as quickly as possible.”
BA’s website was unavailable and some travellers claimed they could not check in on the mobile app, with many venting their frustration on social media. Some have even claimed to have been told by BA staff the company is under ‘cyber attack’.
However, the spokeswoman responded: “We’ve found no evidence that it’s a cyber attack.”
Twitter user Bryan Henson said: “Gate agent at gate A10b just called it a cyber attack…true?”
Michele Andjel added: ‘”It appears it is a cyber attack” said @British_Airways captain @Gatwick_Airport.’
Twitter user Jo Josson also tweeted the cyber attack claims, and said: “Officials are telling us there has been a cyber attack against BA’s systems. Even the tannoy is affected.”
Another flier said on Twitter: “Stuck in Gatwick departures. BA have just announced that it could be a cyber attack that has taken down their systems.”
Heathrow Airport said it was “working closely” with the airline to resolve the issue. In a statement, they said: “We apologise for the current IT systems outage. We are working to resolve the problem as quickly as possible.”
One passenger, Henry Tail, tweeted: “Hey @British_Airways, couldn’t log in to the app with my boarding pass on because systems were down and I missed my flight. What can I do?”
Another, Nadia Whittley, posted: “British airways computers down T5 and standstill, stranded on the plane and they make us pay for food!! Please retweet this indicency! (SIC)”
Julie Adie wrote: “We are on the runway.. For hour now..no offer of drinks..and because ba only takes cards now, we only have cash…wat we supposed to do!!?? (SIC)”
Melissa Davis, who runs MD Communications, a legal PR agency in London, was held for more than an hour and a half on the tarmac at Heathrow, on board a BA flight returning from Belfast.
But by 3pm, the British Airways (BA) plane was still on the tarmac, due to a “technical fault”.
Disgruntled passengers took to social media to vent their frustration at being trapped in the cabin for hours.
One Londoner who was travelling to San Francisco on holiday told the Standard: “They said there was some technical fault with the little truck that tows the plane to the runway.
“So we went back to the gate and they tried to fix it … but then it turned out that wasn’t the problem so they had to try something else.”