The last Concorde to fly has been on show at Filton near Bristol since November 2003 - but tours are to stop because maintenance work needs to be carried out on the jet.
Campaigners fear that because Airbus has set no date for its return that it could disappear from public display forever.
British Airways, which owns the plane, said it had handed over responsibility for it to Airbus who said until it was known what maintenance was needed, a reopening date could not be given.
The plane - Alpha Foxtrot - was built at the Filton works in the 1970s and first flew in April 1979.
It was handed over to British Airways in 1980 where it was in service until its final flight between Heathrow and Filton on 26 November 2003.
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