The five millionth Ford Transit rolled off the production line in 2005
Workers at Ford's Transit van plant in Southampton have been told in a letter future production is "under review".
BBC South's transport correspondent Paul Clifton understands the company is considering cutting production by up to 50% with manufacturing moved abroad.
In a letter sent to employees Ford said "it would be very difficult to continue at the current volume of production".
The company said it was considering future investment but would not comment on any possible job cuts.
In a statement Ford said: "As is usual at this stage in a product cycle, Ford is discussing with employee representatives and union officials plans for future model investment at the Southampton plant."
The Unite union, which represents some of the workers at the factory, said: "Trade unions have been advised of the various scenarios and discussions are continuing to secure the future of the plant."
One worker told the BBC: "I think they might scale down but I don't think it will completely go, that's what we're hoping anyway."
Eastleigh MP Chris Huhne has contacted management of the plant, which employs many of his constituents, to seek clarity on its future.
He said: "If managers do go ahead and cut production as much of what is rumoured, which is 50% with production moving to Turkey, then clearly there will be a lot of job losses locally and a lot of families will be hit."
Ford Transit production moved to Southampton in 1971 and the five millionth vehicle was made in 2005.
The BBC's Mr Clifton added: "In 2005 the future looked secure, but not anymore.
"Staff at the factory talk of terrible morale and several said the factory was being run down.
"Ford has done nothing to dispel fears that production of a British icon will be moved abroad."