UK voters would back remaining in the European Union by 53% to 47% if a referendum was held now, according to a new poll published today.
A YouGov survey for the 'pro-remain People's Vote campaign' found that 45% want a say on the outcome of the Brexit negotiations with 34% opposed.
Exactly half of respondents said the final decision over whether to leave the EU without a deal should be taken by the public in a second referendum, while a quarter said the British parliament should decide.
Opponents of the UK's exit from the EU said the YouGov study of more than 10,000 adults showed public opinion was shifting.
Peter Kellner, a leading pollster and former president of YouGov, said the findings were "politically significant".
He said: "Across the spectrum, the message from voters in this survey is clear - if the government and parliament can't sort out Brexit, the people should".
The 53% to 47% result in favour of remaining in the EU excludes those who do not know how they would vote or would not bother.
A 'no-deal' scenario pushes the six-point margin to 12%, 56% Remain to 44% Leave, the study found.
Nearly three quarters, 73%, believe many of the promises made by the Leave campaign will be broken and 68% fear the UK will end up with a bad deal, with 64% ready to lay the blame on the government.
The poll also found 74% of those questioned believed the negotiations were going badly, while 68% thought that made it likely Britain would get a bad deal.
With less than eight months until Britain is due to leave the EU, British Prime Minister Theresa May has yet to find a proposal to maintain economic ties that pleases both sides of her divided party and is acceptable to negotiators in Brussels.
Mrs May has repeatedly ruled out holding another public vote on Brexit, saying the public spoke in the June, 2016 referendum in which 51.9% of the votes cast backed leaving the EU while 48.1% backed staying.
Last weekend, British trade minister Liam Fox warned he saw a 60% chance of a 'no-deal' Brexit, which would see the world's fifth-largest economy quit the EU on 29 March, 2019 without a trade agreement.