The government says EU rules mean the ships, which are intended to support British aircraft carriers at sea, must be put out to international tender.
However, the French Navy recently announced a €1.7bn contract to build four support ships in France without a competition.
The campaign, called Keep Britain Afloat, is calling on the government to build three new auxiliary Fleet Solid Support ships (FSS) worth £1.5bn in the UK.
A consortium of commercial British shipbuilders is being forced to compete with shipyards from South Korea, Japan, Spain and Italy.
Research conducted by the campaign shows that these shipyards receive direct and hidden subsidies from their governments including, in the case of South Korea, a bankruptcy rescue package.
Thousands of jobs have been lost in the past six months at Rosyth Naval Dockyard, Cammell Laird on Merseyside and in Appledore in Devon, which has been forced to close after 164 years.
Harland and Woolf in Belfast has been put up for sale and there are question marks over the future of Rosyth, Cammell Laird and Fergusons on the Clyde.
Prospect deputy general secretary Garry Graham said: “It is vital we are able protect our ability to design, build and maintain naval ships in the UK. If they don’t, we will lose those skills forever.”
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