BA said that 6,000 employees had decided to take voluntary redundancy, while thousands of others would receive a letter in the coming days to tell them their fate.
Following a selection process, staff will hear whether they still have a job or not, and if they do, whether they will be required to accept a new contract or stay on their old one.
Unite has accused BA of "industrial thuggery" and it is trying to win support from lawmakers to strip BA of airport slots.
BA is currently only flying about 20% of its normal schedule and burning through 20 million pounds per day.
"We are having to make difficult decisions and take every possible action now to protect as many jobs as possible," a spokesman for BA said.
Rival airlines Lufthansa and Air France-KLM have also announced job cuts.
Unite, which has already threatened BA with strike action, called on the airline to offer the same deal that it has agreed with its pilots to other staff.
"We will do everything in our power to prevent compulsory redundancies and attacks on workers' wages by a boardroom with billions in the bank," Unite said in a statement.
British Airways agreed a deal last week with pilots union BALPA for a pay cut of about 20% and some compulsory job cuts estimated around 270.
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