Members of Unite, Unison and the GMB all support calls for the public to be given the chance to decide whether or not to accept a deal, if there is one, or decide whether or not to leave without a deal.
Unison members backed a fresh vote by 66 per cent to 22 per cent, and GMB members by 56 per cent to 33 per cent.
GMB general secretary Tim Roache announced that his union would back another referendum after consulting its 620,000 members.
Peter Kellner, the former president of YouGov, said the results of the poll were significant.
“It’s not that rank and file trade unionists are indulging in gesture politics or ideological breast-beating,” he said.
“They are worried about the impact of Brexit on jobs, taxes, living standards and the National Health Service. They fear that Brexit Britain would find it harder to sell products and services abroad.”
The Independent’s Final Say campaign has the backing of senior members of parliament, including ex-cabinet minister Dominic Grieve, who said it was a “sensible” way out of the UK’s current political crisis.
Labour MP Chuka Umunna and Liberal Democrat MP Layla Moran have also backed the campaign, arguing that giving the public a vote on the final deal was becoming more urgent.
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