The British Airline Pilots' Association (BALPA) has published an open letter describing its "acute embarrassment" over the opening of Heathrow's Terminal 5 and slamming British Airways' "arrogance".
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The union, which represents British Airways pilots, said a change was needed in the way the company was managed.
The letter said, "Failings on the opening days of T5 are symptomatic of BA's loss of focus in delivering a sound operation. This airline can and should make Britain proud but a fundamental change of attitude is required from the very highest levels of BA management.
"It is with great sorrow and acute embarrassment that BA pilots have witnessed the unhappy, distressing shambles that the opening of T5 has become.
"Banks, institutional investors and analysts need to wake up to the fact that there is something very wrong right at the heart of this company that is making our once great brand a laughing stock."
British Airways said in response that chief executive Willy Walsh would not resign, and was "determined to resolve the problems associated with the initial move to Terminal 5."
The letter referred to technical problems that hit the terminal shortly after opening on March 27. Issues with the baggage system and staff familiarisation programmes meant cancelled flights and piles of bags separated from their owners.
British Airways faced more problems over the weekend after icy weather meant more flights had to be cancelled on Monday. There was also another problem with the BAA baggage system leading to cancellations on Saturday and Sunday.