In a joint letter, the former leaders argue that Labour communities have “the most to lose if we leave, but also the most to gain if we remain”.
In a speech at the Hay-on-Wye Festival, Mr Brown was set to say that the Remain camp is relying on non-Conservative supporters - nine million who voted Labour in 2015 and five million backers of other “progressive” parties - for the bulk of the votes it needs to keep the UK in the European Union.
But he will warn that polling suggests a large number of Labour supporters may stay at home, while many of the skilled workers who make up much of the party’s core support are thought to be considering voting Leave.
Mr Brown will call for a “positive, principled and progressive” message to persuade these people to back Remain to support jobs, security and fairness.
“To win the referendum on June 23, the largest Remain vote - perhaps seven to nine million people, depending on turnout - has to come from non-Conservative voters,” the former prime minister is due to say.
“But recent polls suggest that a large number of Labour supporters may not support Remain but instead remain at home.
“In one recent poll, as many as 62% of skilled workers are at risk of voting Leave unless we send out positive messages on employment rights. Why? Because they feel economically insecure, they don’t like the status quo and they need to know that Europe offers something better for their future.”