The airline, which has sole use of Heathrow's showpiece £4.3bn terminal, was planning to launch a heavyweight TV and press campaign next week created by Bartle Bogle Hegarty.
The launch has been cancelled and a new date will be set for later in the year. A spokeswoman said the campaign will roll out once the terminal delivers "the standards of service passengers expect."
By mid-afternoon yesterday, BA had cancelled 33 of the 534 services it planned to operate from the terminal.
In a statement, the company blamed the difficulties on a number of factors, including delays at the staff car park and security hold-ups, which affected baggage handlers.
In the early evening, passengers waiting in Terminal 5's departure hall were told that no one would be permitted to fly with their hold baggage for the remainder of the day.
Other first-day glitches included escalators breaking down and pay machines at the car park not working properly.
The problems are an embarrassment to the airport's owner, BAA, which had hoped the opening of the terminal would bring an end to so-called "Heathrow hassle".