Members of Britain’s three biggest trade unions now support a new referendum on Brexit by a margin of more than two to one, according to a bombshell poll that will cause political shockwaves on the eve of the party conference season.

The survey of more than 2,700 members of Unite, Unison and the GMB by YouGov, for the People’s Vote campaign, also finds that a clear majority of members of the three unions now back staying in the EU, believing Brexit will be bad for jobs and living standards.

The poll comes as union delegates gather in Manchester for the annual TUC conference, where Brexit will be debated on Monday, and two weeks before the Labour party conference in Liverpool, where delegates are expected to debate and vote on Brexit policy. They will also consider calls to keep open the option of a fresh referendum on any deal Theresa May may strike on the UK’s exit from the EU.

Will big three unions back members’ call for a people’s Brexit vote? Read more

In an interview with the Observer before the poll findings were released, shadow chancellor John McDonnell said his preferred option was still for voters to be offered a say on the government’s handling of Brexit – and any deal brought back from Brussels by May – in a general election. But he said that if Labour was unable to force one in the coming months, he wanted to “keep all options open”, including supporting a new referendum.

McDonnell said he was sure there would be a full debate, and votes, on Brexit at the Labour conference. And he went out of his way to praise the People’s Vote campaign, which he said had been very “constructive” and had made clear that its attempts to influence Labour policy should not be seen “as an attack on Jeremy Corbyn or positioning around the leadership. It should be a constructive debate and that is right.”

The poll found that members of Unite, the country’s biggest union, and Labour’s largest financial backer, now support a referendum on the final Brexit deal by 59% to 33% and support staying in the EU by 61% to 35%. GMB’s members support putting the issue back to the people by 56% to 33% and its members want the UK to stay in the EU by 55% to 37%.

Unison members back another referendum by 66% to 22% and would opt to stay in the EU by 61% to 35%.

Union members think standards of living will deteriorate as a result of Brexit by a margin of around four to one (Unite members by 55% to 11%, Unison members by 61% to 16%, and GMB members by 49% to 11%).

They also believe Brexit will worsen, not improve, job opportunities (Unite members by 57% to 16%, Unison members by 52% to 27%, and GMB members by 43% to 18%).

Despite claims that workers are overwhelmingly against immigration, members of all three unions want to prioritise trade over controlling immigration (Unison members by 68% to 22%, Unite members by 65% to 27%, and GMB members by 58% to 32%).

Last week Tim Roache, the GMB’s general secretary, announced that his union would back another referendum after consulting its 620,000 members. Roache, who will address a People’s Vote March for the Many on the opening day of Labour’s conference, said the country did not vote for a “no deal” Brexit or to damage the economy.

“In trade union terms, if we negotiate a pay deal for our members we put that deal back to the members and they decide whether that’s acceptable or not.”

The TUC is expected to adopt a new position on Brexit that will place an emphasis on jobs, rights at work and peace in Northern Ireland. Its executive council is also likely to back the possibility of another vote on Brexit.

Shakira Martin, president of the National Union of Students, who will be speaking at the TUC, said: “What this poll shows is that rank-and-file members of the three largest trade unions in the country are now united in solidarity with young people and students in backing a People’s Vote on the final Brexit deal.

“The campaign for a People’s Vote is a movement that reaches out across regions, party, age, race and class. As we seem to be moving closer to a no-deal scenario which would be disastrous for the country, the time has come to join our voices for a People’s Vote.”

Writing in today’s Observer, Peter Kellner, the former president of YouGov, said the poll could mark a turning point. “It’s not that rank-and-file trade unionists are indulging in gesture politics or ideological breast-beating.

‘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.”

Kellner says the methods used by YouGov are much the same as the company deployed when it correctly predicted Corbyn’s win in the race for the Labour leadership in 2015.

Baroness Margaret Prosser, a Labour peer and former president of the TUC, said: “Trade unions always listen to members and that’s why we’re already beginning to see them move on this issue. But this poll is important because it shows we need to move further and faster in the next few weeks if we’re going to fight for the best interests of workers.

“A People’s Vote is the last, best hope we have of preventing massive damage on jobs, public services and our most hard-pressed communities.”

Conservative MP and former minister Guto Bebb, who quit as a defence minister in July in protest at Theresa May’s concessions to Tory Brexiters, yesterday added his voice to those backing another referendum.