Wednesday's woes are the latest in a string of problems at the airline, which is also smarting from a $230 million fine this month for a huge customer data breach and is bracing for potential strikes in a pay dispute with its pilots.
BA, owned by International Airlines Group, apologised to customers for Wednesday's disruption and said its technical team was working to resolve the problems as soon as possible. It urged customers to allow extra time at airports.
Dozens of flights were cancelled or delayed, including flights to Greece, Spain, Italy and Russia, according to the departure boards at British airports.
BA would not confirm how many people have been affected by the IT problems but said that it was experiencing a "systems issue" affecting check-in and flight departures at Heathrow, Gatwick and London City airports.
Customers have experienced issues checking in online, while others complained of being stuck on planes unable to take off for hours.
Stuart Jackson, a photography business manager, said he was stuck on a grounded plane at Heathrow and had already missed his connecting flight, disrupting months of planning and wasting thousands of pounds.
"When I do arrive, I will have to just fly home again," he said on Twitter. "BA is a complete catastrophe and I will never fly with them again."
A little more than a year ago BA was forced to cancel flights at Heathrow, Europe's biggest airport, after problems with a supplier's IT system. And in May 2017 a massive computer system failure because of a power supply issue left 75,000 customers stranded.
British Airways said it has moved to back-up manual systems to keep some flights operating and it is offering customers the chance to rebook for another day.Customers, meanwhile, continued to take to social media to voice their anger.
Jamie Boswell said his flight was cancelled while he was attempting to check in. "Very busy to rebook. Not ideal with a one-year-old," he said.
About half of the British Airways flights scheduled to depart from Heathrow's terminal five between 0930 and midday were cancelled or delayed, according to the airport's website.