The airline said it was "extremely disappointed" at the union's decision, adding that it would cause massive disruption to hundreds of thousands of travellers in the run-up to Easter.
Workers are unhappy about changes that include a pay freeze in 2010, a switch to part-time work for 3,000 staff and a reduction in cabin crew sizes on long-haul flights.
BA says the changes are necessary for the airline to cope with a downturn in passenger demand due to the global financial crisis.
The airline has been training around 1,000 workers from other departments to stand in for cabin crew in the event of a walkout.
It said on Friday that it was also working to obtain seats on flights operated by rival airlines to pass on to its own customers.
"Should a strike take place, we will do everything we can to protect our customers' travel plans as far as possible,'' BA said in a statement.