"While we have never wanted this dispute, it is a disgraceful day for democracy when a court can overrule such an overwhelming decision by employees taken in a secret ballot," they said.
The original ballot saw 92.5% of those balloted vote in favour of industrial action.
Bob Atkinson of travel website travelsupermarket.com said the one million passengers booked to travel with BA over Christmas and the new year "can now breathe a sigh of relief and carry on with their travel plans".
"BA should now contact customers as soon as possible to confirm flights will be going ahead and normality has returned to the market," he added.
"The threat of strike action has been hugely damaging for the British Airways brand and customer loyalty has been tested."
One BA cabin crew worker contacted the BBC to say she was "delighted" the strike had been stopped.
"I voted for the strike but never dreamt it would be for 12 days over Christmas," she said.
"I'm delighted it's been stopped, we have the upmost respect and regard for our customers and I'm glad we have the opportunity to show this over the festive season."
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