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.
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.
Figures showed that 45% of people thought Brexit would be good for immigration levels, while 24% said it would be bad, and 31% said it would make no difference.
And 42% said immigration more generally has had a positive influence on Britain.
Former Ukip leader Nigel Farage said: “Funny isn’t it? On the one hand we are being told Brexit has made people hostile towards migrants, on the other we are told we are more relaxed about it.
“You can’t have it both ways. The truth of it is, the reason those figures have changed is a big chunk of the electorate think the immigration issue has been dealt with because we voted Brexit, and they think our major political parties will carry out their wishes.
“Actually, the penny’s not yet dropped. That there is no intention for this Government or this opposition to deal with open door immigration.”
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.
However, while it was backed by 63% of people who voted Remain, it was backed by just 20% of Leave voters.