Figures shared with the Scotsman show that just 49.2 per cent of Labour voters at the last general election would keep faith with the party in a snap vote, which could come as early as November.
Amid a furious row at the party’s conference in Brighton, Labour members will be asked today to endorse Mr Corbyn’s neutral stance or back calls from most of its activists and shadow cabinet members to back Remain.
Scottish Labour leader Richard Leonard weighed in, saying he wants the party to take a Remain stance.
The polling, carried out by trade unions, suggests the Labour vote in Scotland would be the worst hit of any part of the UK, putting the party on course for another wipeout on the scale of the 2015 general election.
The figures were cited by Shadow Foreign Secretary Emily Thornberry, who intervened in Labour’s growing row over Brexit to say she was “fearful” of Boris Johnson staying in Downing Street for another five years unless Labour unequivocally backs EU membership.
Ms Thornberry warned Labour would only be given a hearing on its social and economic policies in a snap election if it was clear on Brexit.
“I do think we suffered in the European elections by not being sufficiently clear, and my view is that we are not being sufficiently clear now,” she said.
Ms Thornberry described Labour’s position as “a little bit like that scene in Star Wars, where they’re in the garbage crusher and the walls are coming in on either side.
“You don’t just stand there and say ‘it’s alright’, you have to get out of there. If we don’t, I’m fearful for the result of the general election.”
Trade unions polled voters earlier this year on Labour’s current policy of putting a new Brexit deal it negotiates to a referendum, with Remain on the ballot paper but with Labour going into a general election without a clear stance on which option it would campaign for.
Across the UK, only 58.7 per cent of 2017 Labour voters would stick with the party under those circumstances. The Lib Dems would take 19 per cent of the 2017 Labour vote, with 7.4 per cent going to the Greens, 3.5 per cent to the SNP, and 0.7 per cent to Plaid Cymru.
That compares with 7 per cent going to the Brexit Party and 4 per cent to the Conservatives.
The figures are even worse in Scotland, where just 49.2 per cent of 2017 Labour voters would stick with the party. The SNP would take a fifth of Labour’s vote at the last election, with 15% going to the Lib Dems, 6% to the Brexit Party, and 3% to the Conservatives.
Ms Thornberry insisted her comments were not part of a leadership bid amid growing speculation about a fresh challenge to Mr Corbyn’s authority.
“In a polarised situation like this, it’s absolutely right to keep the country together, which is what a second referendum does in my view, but we’ve got to be honest about who we are - and we’re internationalists and Europeans,” Ms Thornberry added.
“I know that the scottish Labour Party agreed with me, and I know that the Welsh Labour Party agree with me.
“There are so many marginal seats in Scotland. I hear the stats and my heart misses a beat, because I was first elected on a majority of 484.
“There are lots of seats that are really marginal on all sides, which is why it’s so important that we are clear.”
Ms Thornberry’s intervention follows a call from Scottish Labour leader Richard Leonard for the UK party to follow policy set north of the border and in Wales, backing Remain in the event of a second EU referendum.
Mr Corbyn is under pressure ahead of a vote of members in Brighton tomorrow, after he said he would “go along with whatever decision the party comes to” at a special conference to decide Labour’s stance in a referendum.
Pressure was also heaped on the Labour leader by the London Mayor, Sadiq Khan, who told a fringe event in Brighton: “Staying neutral in the face of the biggest economic and social threat to our country for decades is simply not an option.”
Mr Corbyn defended his ‘neutral’ stance and promised a special Labour conference for party members to decide whether to endorse a new Brexit deal his government would negotiate, or back Remaining in the EU.
“What we have said is that we would want to hold a consultation, a special conference of our party at the point that we have got this offer from the EU, we’ve got this as a remain - and hopefully reform - option,” he told the BBC’s Andrew Marr show.
“Because I do think even those that are strongly in favour of remain would recognise the EU needs to have some reforms.”
The Labour leader said he would “go along with whatever decision the party comes to” on Brexit, and did not rule out giving Labour MPs a free vote if Boris Johnson brings a deal back to the Commons.
Mr Corbyn risked angering Labour’s pro-EU membership by suggesting the UK could be better off after Brexit, with the right deal.
“Please remember why people voted Leave, why people voted Remain, but also remember there is more that unites all of those people – over austerity, over investment, over education, over housing, over health, over a green industrial revolution – than there is that divides them,” he said.
Conservative Party chairman James Cleverly said the comments show Mr Corbyn “can’t lead his own party”.
“Jeremy Corbyn this morning refused nine times to say if Labour would support Brexit even if they negotiated a deal with the EU themselves, showing Labour offer nothing but dither and pointless delay,” Mr Cleverly said.
“Jeremy Corbyn can’t lead his own party, let alone the country – he can’t even make up his mind on the most important issue facing the country.
“He would delay Brexit until at least 2020 and even longer if the EU demand it – Brussels would be in the driving seat and Corbyn would accept anything from them.”
Liberal Democrat Brexit spokesman Tom Brake, whose party has pledged to revoke Article 50 if it forms a majority government, said: “Jeremy Corbyn has once again refused to deny that if he becomes Prime Minister his government will be a Brexit government.
“This will be deeply concerning to millions of Labour supporters who want to campaign to stop Brexit and cannot get any clarity from Labour.”