Luggage check-in was suspended on the opening day
Further chaos is expected at Heathrow's Terminal 5 after its opening day was marred by a catalogue of errors which left many stranded overnight.
So far, more than 30 departures have been cancelled, queues are building and frustrated passengers have missed flights - blaming lack of information.
In addition, some of Saturday's flights are expected to be cancelled.
BA chief executive Willie Walsh accepted the debacle had affected the reputation of BA and of Britain.
"It was not our finest hour.
"We clearly disappointed a number of people and we sincerely apologise," he said.
He said a "combination of factors" they had been unable to "get on top of" had led to the disruption.
"British Airways has not delivered and we need to deliver," he said. "I am accepting responsibility, the buck stops with me."
He said: "Today has started much better," but added: "At this stage I still expect some cancellations tomorrow".
British Airways says it plans to operate 80% of flights.
According to the airline's website, 36 of Friday's flights from T5 have been cancelled.
The airline advised customers to check its website, www.ba.com, for service updates.
Many passengers say they have missed their flights with some blaming a lack of desks open to cope with the number of people and the wrong information given out.
First day chaos
The airline, which has sole use of T5, says it has drafted in extra staff and held meetings through the night to try and ease the problems that wrecked the terminal's first day.
On its first day of operation, hold luggage services were suspended as a result of a baggage backlog, 34 flights were cancelled and passengers had to wait up to four hours to reclaim their luggage.
Some stranded travellers spent the night on the floor of the new building.
One baggage handler told BBC News what should have been BA's greatest hour had "turned into a shambles the moment the doors opened".
36 domestic flights cancelledLong-haul flights operatingPassengers will be able to check in with both hand and hold baggageBA information line - 0800 727800
"BA claimed 'staff familiarisation' was to blame. The staff, however, would blame the lack of training and the essential support that was promised.
"During the inadequate training days prior to the opening, any staff questions were bounced back with 'I don't know' and 'It will be clear on the day'.
"Staff signage is non-existent and quite frankly, how are we expected to help customers if we are not helped first?"
Passengers on Thursday's cancelled flights were offered £100 towards the cost of overnight accommodation by the airline, but travellers reported that local hotels were charging up to twice that figure.
In a statement, the company said the backlog had been caused by a number of factors, including delays at the staff car park and security hold-ups which affected baggage handlers.
Local Conservative MP David Wilshire, who serves on the Commons Transport Committee, said it was not clear who was to blame - BA or the airport's owner, BAA.
"The problem is getting to the real truth of this.
"'Not my fault, guv, maybe his fault guv' is, I think, a bit of the problem," Mr Wilshire said.
"And we won't get to the bottom of this until we know a bit more. What we have to find out is why this has happened and make sure it's put right and hope that this is really a starting glitch. People have been let down, let's be honest about it."
The suspension of luggage check-in was not the only problem to hit passengers hoping to leave T5 on its opening day.
BA earlier announced that "initial teething problems" with car parking provision, delays in staff security screening and staff familiarisation had resulted in a backlog of baggage.
This led the airline to cancel a number of flights in and out of the terminal, including services to Munich, Frankfurt, Paris and Brussels as well as Edinburgh, Glasgow and Aberdeen.
A further technical fault also meant seven flights left T5 without luggage on board.
The BBC's transport correspondent Tom Symonds said the backlog was caused by problems with the airport's luggage processing system.
An underground conveyor system had become clogged up, he said.
This was being blamed on staff failing to remove luggage quickly enough at the final unloading stage.
In a statement, the Department for Transport said it expected BA and airport operator BAA "to work hard to resolve these issues and limit disruption to passengers".
BA has set up an information line for T5 passengers: 0800 727800
Have you been through Terminal 5 today? What was it like? Do you work there? Tell us about the new terminal at Heathrow airport.
You can send pictures and video to: firstname.lastname@example.org or to send via MMS please dial 61124.
Do not endanger yourself or others, take any unnecessary risks or infringe any laws.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.