Union members would be overwhelmingly more likely to vote Labour if the party gives them the chance to back remain in a second referendum.
A new poll for the People’s Vote campaign found 64% of union members back having a referendum, compared to 33% against.
And if there is a new referendum 71% of union members would support staying in the EU, the poll claimed.
The YouGov poll of 1,813 trade unionists also found they were more likely to back than abandon Labour if the party backs a ‘People’s Vote’.
Among those who said it would make a difference, 35% said backing a referendum would make them more likely to vote Labour. 12% said it would make them less likely to back the party.
Left-wing anti-Brexit activists have also ramped up pressure on Labour to whole-heartedly back a second referendum and Remain.
The group Another Europe is Possible is launching a campaign called Remain Reform Revolt with public events in Nottingham on July 12, London on July 13, Birmingham on July 24 and Leeds on July 27.
The group has also drafted an anti-Brexit motion by almost 300 local Labour parties which could be debated at the party conference in September.
Labour elections chief Andrew Gwynne admitted the party’s switch to backing a second referendum on any Brexit deal is “a difficult message.”
But speaking on Sunday morning, he confirmed Labour would demand any new Brexit deal be put to a public vote.
He said: “Any Brexit deal that is brought to Parliament, including a no deal scenario, we will say as the Labour Party that there should be a second referendum on those prospects.
“Because it’s looking increasingly likely that we’re heading to no deal – that was not on the ballot paper in 2016.”
Jo Stevens, the Secretary of the Trade Union Group of Labour MPs and a leading supporter of the People’s Vote campaign, said: “Labour is moving to giving the people the final say on Brexit and campaigning to stay.
“This is the right thing to do for our economy, jobs and our internationalist outward-looking trade union and Labour values.
“But Labour’s official position is still too far behind that of our party members and voters, not to mention grassroots trade unionists who are the bedrock of our movement.”
Jeremy Corbyn said last week that Labour would back a “public vote” on any Brexit deal, a move senior Labour figures described as a “staging post” towards a more explicit policy.
But Labour MPs in Leave seats have been resisting the party’s push to a second referendum.
One, Caroline Flint, said today it was “pretty clear” 26 Labour MPs would vote against any push for a second referendum in Parliament.
She said she was still “optimistic” Parliament could reach a deal adding: “The health of the nation needs us to agree a deal and move on.”
Asked if she would vote for a no-deal Brexit or staying in the EU, Ms Flint told BBC1’s The Andrew Marr Show: “I won’t be voting to revoke Article 50.”
Pressed on whether that meant she would back a no-deal Brexit, Ms Flint said: “If that is where we end up, that is where I will be.”
Unite questioned the findings of the poll.
A spokesman for the union said: “Polls that profess to speak for our members yet are not conducted by our union cannot be considered credible.
“This tactic has never worked before and won’t work now.”