Hundreds of people woke up at Heathrow Airport's Terminal 5 or hotels on Friday after being stranded by the chaos of the opening day.
On Thursday 34 flights were cancelled, followed by 36 on Friday, with many more cancellations expected over the weekend.
The "teething problems" were blamed on a number of factors including staff car-parking problems and staff security screening.
BA chief executive Willie Walsh said it "was not our finest hour" and the debacle had affected both the airline's and Britain's reputations.
He said a combination of factors they had been unable to "get on top of" had caused the disruption.
Check-in of luggage was suspended on Thursday, after an underground conveyor system became clogged up.
British Airways has set up an information line for passengers expecting to use T5, the number is 0800 727800.