Judge Laura Cox of the High Court in London issued the order two days after the strike was called by an overwhelming majority of the airline's 14,000 crew members, CNN reported Thursday.
Unite union leaders said the ruling marked "a disgraceful day for democracy."
In a statement, the airline said it was "delighted for our customers," an estimated 900,000 of whom would have been inconvenienced by canceled flights.
BA's attorney Bruce Carr told the court the voting process included "serious and substantial irregularities." In addition, he said a strike in the holiday travel season was "willfully disproportionate and clearly unlawful."
The strike was one of several potential disruptions of travel services in Britain this month.
Scottish charter company Globespan canceled all its Flyglobespan flights as it went into administration -- a step similar to bankruptcy.
In separate strike action, Unite baggage handlers and check-in clerks at Heathrow and Aberdeen airports plan three work stoppages lasting two and three days through Jan. 4 over pay issues.
British Eurostar drivers have also called for four days of strikes, scheduled for Dec. 18-19 and Dec. 26-27, but Eurostar said service would not be disrupted, as other train drivers were available.
Copyright 2009 by United Press International.
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