The unprecedented survey, which included 17,000 responses in Scotland, shows that a significant majority want the UK to stay in the European single market and believe Britain will be economically worse off outside the EU.

If a referendum were held tomorrow, survey data collected from readers of three major newspaper groups suggests the Remain side would win by 51 per cent to 49 per cent once “don’t knows” are removed.

The findings come as Prime Minister Theresa May faces growing pressure from within her own party not to concede on her Brexit “red lines” of leaving the single market and customs union.

A new Brexit poll has shown Britain would narrowly vote to stay in the EU if a new referendum was held next week.. Picture: PA Wire

Brexiteer MPs voiced their anger over the weekend following reports that the EU has rejected British compromises to keep the Irish border open, a move that would leave the “backstop” of continued customs union membership as the only possible option.

Almost 220,000 readers of titles belonging to Scotsman publisher Johnston Press, as well as newspaper groups Newsquest and Trinity Mirror, took part in the online Brexit survey with Google Consumer Surveys.

Views were collected from readers of newspapers and websites from the Stornoway Gazette to the Bexhill Observer, including major titles such as the Manchester Evening News, the Yorkshire Post and the Western Mail.

The survey found that across the UK, 52 per cent of respondents believe Britain would be economically better off inside the EU, with 56 per cent calling for a “soft Brexit” inside the single market - including more than a fifth of Leave voters.

However, views remain polarised, with just 9 per cent of Leave voters taking part believing EU membership is better for the UK economy, compared to 85 per cent of Remain voters.

Leave voters are twice as likely to have changed their mind since the 2016 EU referendum, giving pro-EU campaigners a boost in the event of a second referendum on the terms of the UK’s Brexit deal.

People in Scotland were most likely to say Britain would be economically better off inside Europe, at 63 per cent, including 13 per cent of Leave voters. They were also the most likely to say that Britain should stay in the single market, at 66 per cent.

Stephen Gethins MP, the SNP’s Europe spokesman, said the survey showed opposition to a “cliff edge” Brexit.

“This shows hardening opposition across Scotland to the Tories’ hard Brexit shambles, even among Leave voters,” Mr Gethins said.

“The UK government must listen and change course before they really take us to the cliff edge.

‘’They can no longer continue being deaf to the growing chorus of calls to protect jobs, investment and living standards – we should remain in the customs union and the European single market, which is around eight times bigger than the UK’s alone.

“Theresa May must stop pandering to the extreme Tory Brexiteers, whose agenda will do untold damage to the economy and jobs for many years to come.”

Yesterday the shadow Foreign Secretary Emily Thornberry said Labour’s policy of negotiating continued membership of a customs union with the EU after Brexit was the only way to protect trade and avoid a hard border in Northern Ireland.

“There is nowhere else we can go than to stay in a customs union with the European Union,” she told the BBC’s Andrew Marr show. “Nothing else makes sense.”

Among the 8,200 people in Northern Ireland who responded to the survey, 67 per cent said any customs checks at the border with the Republic after Brexit would be unacceptable - including 34 per cent of Leave voters in the province.

Responding to the survey, Scottish Labour Brexit spokesman Neil Findlay MSP said: “The Tories handling of Brexit has been nothing short of shambolic.

“It is clear that the majority of voters in Northern Ireland oppose a hard border and voters across Britain do not buy into the bargain basement Brexit that the Tories are trying to sell them.

“The Tories are incapable of delivering a Brexit that is good for Scotland or working people across Britain, with some jobs already under threat or lost due to their ignorant mishandling of the situation.

“That is why Labour wants to see a strong and close ongoing relationship with the EU including a new permanent customs union, which protects tariff free trade and the Good Friday Agreement.”

The survey also promises to fuel the debate within Labour over whether the party should back remaining a member of the single market after Brexit.

Yesterday Owen Smith, the former shadow Northern Ireland Secretary sacked last month by Jeremy Corbyn after calling for a referendum on the terms of the UK’s Brexit deal, said “nobody serious” believes the Irish border issue can be resolved without staying in the EU trading bloc.

“I think I said what most Labour members, what most Labour supporters think, which is that Brexit is not the right choice for our country, that we can see massive costs and complications now associated with it,” he told ITV’s Peston on Sunday programme when asked about his sacking.

“Northern Ireland is probably the best example of that. Nobody thought that there was any prospect of even a risk of conflict in Northern Ireland as a result of Brexit, but that is precisely where we are... nobody serious thinks this can be done without staying not just in the customs union, but the single market.”

Edinburgh South MP Ian Murray, the co-chair of the Scottish Labour for the Single Market campaign, said the findings were “hugely significant” and should serve as a “wake-up call to Scottish Labour and the UK leadership”.

“More than two-thirds of voters want the UK to remain in the single market because they know 80,000 jobs in Scotland depend on it, it delivers hard-won rights for hundreds of thousands of workers, and is the only way to prevent a hard border with Ireland,” Mr Murray said.

“There is no such thing as a good Brexit, but the least-worst option for our economy and for jobs is permanent membership of the Single Market and the Customs Union.

“Time is running out for Labour to stand up for the people we represent and ensure we defeat Theresa May’s plans for a hard Brexit.”

Major survey finds Remain would win second Brexit referendum