The Conservative leader and Brendan Barber, the former head of the Trades Union Congress (TUC) umbrella body, said the stakes were so high in the June 23 referendum that "it is right that the rules of conventional politics be temporarily set aside".
In a joint article in The Guardian, they warned that the "economic shock" of a Brexit would see unemployment rise, growth fall, less open trading leading to lower productivity and lower wages, and put pressure on the pound, leading to more expensive goods.
The article comes after the government made a series of concessions to the controversial Trade Union Bill, including on a measure that would have cut union funding.
It prompted speculation that ministers had struck a deal with the unions to take a more vocal role in the EU campaign. Downing Street said the two issues were separate.
Almost a dozen unions representing around four million workers, including the biggest, Unite, back the "Remain" camp, as does opposition Labour leader Jeremy Corbyn.
Opinion polls suggest the public is divided on the issue of whether to stay in or leave the EU, although the "Remain" side has a slight lead and up to one fifth remain undecided with less than two months to go.
