The airline said it had found "no evidence that it's a cyber attack".
"We have experienced a major IT system failure that is causing very severe disruption to our flight operations worldwide," BA said in a statement.
"The terminals at Heathrow and Gatwick have become extremely congested and we have cancelled all flights from Heathrow and Gatwick before 6.00 pm UK time today (1700 GMT), so please do not come to the airports."
The airline had suffered previous IT glitches, with passengers hit by severe delays in July and September last year.
Distressed passengers immediately took to Twitter expressing their discomfort, several said that they were unable to check in or use the airline's app while others were left grounded on the tarmac.