Fresh BA strikes are set to go ahead next week after a panel of judges overturned a ban on industrial action.
BA was granted an injunction on Monday after the High Court ruled that the Unite union had not reported results of its strike ballot correctly to members.
Unite's success means a series of five-day strikes will start on Monday unless an agreement can be found.
"We shouldn't have been in this process," said Unite's Derek Simpson. BA was "disappointed" with the ruling.
The panel ruled 2-1 in favour of overturning the injunction.
The Lord Chief Justice, Lord Judge, and Lady Justice Smith upheld Unite's appeal. The Master of the Rolls, Lord Neuberger, rejected it.
In addition to the five-day strike starting on 24 May, two more five-day stoppages are due to begin on 30 May and 5 June.
BA said it would run a full schedule at Gatwick and London City airports. At Heathrow, it said it would operate more than 60% of long-haul flights and more than 50% of short-haul flights.
Unite members outside the court sang "we are the champions" after the verdict was announced.
But Mr Simpson, Unite's joint leader, said: "This is not a moment for being triumphant. We shouldn't have been in this process.
"The case brought by BA was trivial and, in my opinion, irresponsible."
A joint statement from Mr Simpson and Unite's other leader Tony Woodley called on BA to "seize the possibility for industrial peace".
"We hope it has the wisdom to do so. Failing that, cabin crew will once more be taking industrial action with our full support," they said.
The two sides have been involved in a long-running dispute over pay, jobs and working conditions.
But Unite says the stumbling blocks now are travel perks that were taken away from members who went on strike in March and disciplinary action taken against more than 50 of its members.
Conciliation service Acas said it hoped BA and Unite would reopen talks directly, adding that its facilities were always available if needed.
BA said it was "disappointed for our customers" that Unite's appeal had been upheld.
"We will implement our contingency plan to keep British Airways flying," the company said in a statement.
"We are confident that thousands of cabin crew will ignore Unite's strike call and help us fly more than 70% of the customers who were booked to fly with us in the period targeted."
The ruling in favour of BA on Monday meant that Unite's first planned strike, scheduled to begin on Tuesday, ending on 22 May, could not go ahead.
Despite this, flights have been disrupted this week as the airline was unable to reinstate all services.
"Unite's strikes have failed twice and they will fail again," BA added, referring to this week's injunction and one the airline won in December, preventing cabin crew from striking over Christmas.