Woolwich barracks have been earmarked for closure following a spending review by Sevenoaks MP and secretary of state for defence Michael Fallon.
The Grade II* historic site could be closed by 2028 as the Ministry of Defence battles to make savings.
The building in Repository Road has been in use since 1802 and is one of 91 properties set for by the MoD.
Fusilier Lee Rigby was attacked and murdered by extremists close to the barracks in May 2013.
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