"The CSEU will work constructively with the company to keep redundancies to a minimum and ensure no compulsory redundancies," said the union's general secretary Hugh Scullion.
"The CSEU believe there is still an opportunity to extend production at the Woodford site."
BAE said the Woodford site was likely to close at the end of 2012, following the completion of its contract to build the latest version of the RAF's Nimrod maritime patrol aircraft.
"It has been clear since 2003 that the Woodford site had little future beyond the end of the Nimrod MRA4 production, and the workforce has been kept informed since that time," said the company.
A spokesman for the Ministry of Defence said that while "job losses are always to be regretted and are most unfortunate for those affected", BAE's announcement was "a commercial matter for the company".
Kevin Taylor, BAE's managing director of military air solutions, said the company would work with employees "to explore ways of mitigating these potential job losses".
"Whilst we regret having to make this announcement, we have to ensure we are the right size and shape to remain competitive and meet our customers' requirements for the future."
The Woodford factory has a rich history of aircraft manufacture, building more than 4,000 Lancaster bombers during World War II, and the delta-wing Vulcan bomber in the 1950s.
"My father worked here before me, and I have been here for 29 years, so it is a sad day," said Andy Jackson, a logistics operator.
"But the announcement is not unexpected, we have been building up to it for about a year now.
"It is not like we will be thrown out of work instantly, we have got several years to plan our future."
BAE's latest job cuts announcement comes five months after the firm said it was trimming 500 positions and closing sites in Telford, Leeds and Guildford.
BAE revealed in July that its pension deficit had widened sharply to £3.1bn in the six months to 30 June.
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