The survey, which polled 4,119 members of the four largest UK parties, found eight out of 10 Labour members either agree or strongly agree with having a second vote – something Mr Corbyn has ruled out.
The survey by the Mile End Institute at Queen Mary University in London, found not only did 78 per cent of Labour members want a second Brexit referendum, support for such a step among the Liberal Democrats and Scottish National Party (SNP) is even stronger.
Among the pro-EU Lib Dem grassroots, 91 per cent want a second say on the country’s breakaway from the European Union, along with 87 per cent of SNP members questioned.
Just 14 per cent of Prime Minister Theresa May’s Conservatives think there should be a public vote on the final deal.
On membership of the EU’s customs union, 95 per cent of Lib Dem members, 91 per cent of SNP members and 85 per cent of Labour members wish to remain within it, while the equivalent figures for the EU single market are 96 per cent, 95 per cent and 87 per cent.
Just 27 per cent of Tory members want to stay in the customs union and 25 per cent wish to stay in the single market – reflecting the Government’s policy of leaving both after Brexit.
Tory members also adopted a harder line on immigration, with 83 per cent agreeing that all EU member countries’ nationals should be subject to the same immigration rules as non-EU nationals. Among Labour, 33 per cent agreed with the proposition.
The poll results come as former Prime Minister and arch-Remainer Tony Blair said Britain needed a second referendum because people “didn’t know what the terms of the new relationship will be”.
He claimed in an interview on the BBC Radio 4 Today programme: “It is not undemocratic to say we should be entitled to think again.”
In a separate interview on the Today programme, Mr Blair claimed he “accepted entirely” the electorate’s verdict to leave but went on to insist: “Democracy doesn’t just stop for one day.”
He added: ”You could have an election on the issue.
“You can have a debate about how much but there is little doubt that Brexit is causing economic difficulty.”