About 1,000 workers will lose their jobs at Dagenham near London while 500 jobs will go at the plant in Southampton on the south coast of England where Transit vans are made, the GMB union said.
GMB national officer Justin Bowden said: "This is devastating news for the workforce in Southampton and Dagenham. It's also devastating news for UK manufacturing."
Bowden added that "Ford's track record in Britain is one of broken promises and factory closures."
The Southampton plant has made about 2.2 million Transit vans since 1972, but its workforce has been steadily reduced over the years, as production slumped from 66,000 vehicles in 2008 to 28,000 last year.
Member of parliament John Denham, who represents Southampton for the opposition Labor party, said it would be "devastating" if the factory closed.
"Huge numbers of families would be affected. It would also be very bad for the UK motor industry," he told the BBC.
"Obviously, we hope it's not true but it would be devastating if it closed, there are hundreds of jobs that depend directly on the plant and many others in the local economy.
"Southampton is the only place that still makes complete Ford vehicles of any type in the UK," said Denham.
Ford employs around 11,400 workers in Britain at plants including Dagenham in Essex, Halewood on Merseyside in northwest England and Bridgend in south Wales.
In France, the number two European carmaker after German VW, PSA Peugeot Citroen, has already announced the loss of 8,000 jobs and the closure of a factory.
Copyright Agence France-Presse, 2012