Meanwhile, 5,751 of Unite union’s members have voted for industrial action against the airline, compared to 1,579 against. Unite said 72% of its 10,000 cabin crew members had voted.
The Unite dispute, originally over job cuts, has already cost BA £150m and led to 22 days of strikes.
The issues originally began in November 2009, when BA reduced the number of cabin crew on long-haul flights, and introduced a two-year pay freeze from 2010.
However, the most recent ballot was in protest against the removal of travel perks from staff who went on strike last year.
Unite’s leader Len McCluskey said: "For the fourth time in 13 months, BA cabin crew have voted overwhelmingly in support of their union and expressed their dissatisfaction with management behaviour."
If strikes go ahead, they could take place over the bank holiday weekends in April.
A BA spokesman said: "We urge Unite to return to the deal we negotiated, which guarantees pay rises for the next two years and secures terms and conditions for our existing crew that are the best in the UK industry."