Remain would win a new Brexit poll by 54%-46%, according to analysis of one of the largest surveys carried out on the issue.
Some 20,000 people were questioned in a Survation poll for Channel 4 which estimated 105 local authority areas that voted Leave in 2016 would now be carried by the Remain side.
Channel Four said a “multi-level” modelling technique, which successfully predicted the 2017 general election result, had been used in the exercise.
In a no-deal scenario, a majority of voters would back staying in the EU, at least temporarily, according to the poll.
The survey found that in a no-deal situation 35% believe Britain should remain in the EU, while 19% would want to delay leaving to allow more time for talks, and 36% would wish to quit the bloc.
Asked how they would vote if the government secured a deal and it was put to the people, 33% said they would reject it, 26% accept it, 34% did not know, and 7% indicated they would not vote.
Justice secretary David Gauke told the Channel 4 programme that revealed the results: “If we leave on no-deal terms there’s is no good shying away, it will be very bad for us economically.
“If we can get a good deal, and that means removing all the frictions. The Chequers-type deal, as I say, if we don’t have friction with trade, then, economically, I don’t think it’s going to make a particular big difference one way or the other.”
The modelling technique showed that support for leaving the EU has fallen most dramatically in the local authorities areas that saw the highest leave vote shares in 2016.
Some 43% said they would support a second referendum that was a binary choice between a deal and staying in, with 37% opposing a vote on those terms.
But while it was backed by 63% of people who voted Remain, it was backed by just 20% of Leave voters.
Liberal Democrat MP Tom Brake, a champion of the anti-Brexit campaign group Best for Britain, said the will of the people was “not set in aspic”.
He said: “This poll, the largest of its kind, shows that as Brexit unravels and the benefits of EU membership become clearer, the appetite for Remain grows.
“This poll feels like a turning point to me.
“But there is only one way to test the scale of this change and that is through a People’s Vote.”