The UK's flag carrier apologised for the "global system outage" and said it was "working to resolve the the problem as quickly as possible".
Heathrow Airport said it was "working closely" with British Airways to solve the issue.
It is not known how many flights have been affected but passengers have reported issues with flights to and from Heathrow, Gatwick and Belfast.
British Airways aircraft landing at Heathrow are unable to park up as outbound aircraft cannot vacate the gates, which has resulted in passengers being stuck on aircraft.
Heathrow has advised passengers to check the status of their flights before travelling to the airport.
Around the world planes were grounded and passengers stuck either in terminal buildings or on planes themselves, as a shortage of available gates meant incoming passengers had no opportunity to disembark, 'The Telegraph' reported.
"We're experiencing a global system outage," said the company in a reply to one disgruntled traveler on Twitter.
Customers across the world have been tweeting the company complaining they have been waiting to get off their flights for up to three hours.
"British airways computers down T5 and standstill, stranded on the plane and they make us pay for food!! Please retweet this indicency! (SIC)", another Nadia Whittley posted.
"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)", Julie Adie wrote.
"An issue with a worldwide British Airways' IT system is causing some delays for passengers at Heathrow this morning," said a spokesman for Heathrow, where queues at Terminal 5 were described as "catastrophic".
British Airways passengers faced severe delays in July and September last year because of problems with the airline's online check-in systems.
British Airways is the flag carrier and the largest airline in the UK based on fleet size. When measured by passengers carried, it is second-largest in the country behind easyJet.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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