The stark YouGov survey found that just two Tory-held constituencies, Broxbourne and Christchurch, favour Ms May’s blueprint, compared to 30 seats that prefer a no-deal Brexit and 600 areas that put staying in the EU as their first preference.
The prime minister is engaged in a frantic push to sell her deal to sceptical MPs and the public, ahead of a crunch vote on Tuesday which could threaten her leadership and her government.
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After a flurry of media appearances to appeal to the public, Ms May also signalled that parliament could be given the power to decide whether the UK goes into a controversial Irish backstop, as a last-ditch effort to win over wavering MPs.
Pollsters asked more than 20,900 people in Britain to rank the PM’s deal, no deal and remaining in the EU in order of preference, which revealed the overwhelming majority of constituencies would put remaining in the EU as their first choice.
Staying in the EU gains 46 per cent of national support, while Ms May’s deal and no deal were level on 27 per cent each, the poll found.
The deal is failing to curry favour among either Remain or Leave voters, as the survey found that less than half (40 per cent) of Brexit voters support her deal, while 51 per cent prefer no deal.
Of Remain voters, only 13 per cent support the prime minister’s deal, with the vast majority (83 per cent) still favouring staying in the EU.
However, if Ms May’s deal is pitted against no-deal Brexit then it garners more support, winning by 65 per cent compared to 35 per cent.
Meanwhile, staying in the EU and Ms May’s deal are even on 50 per cent when compared to one another.
If remaining in the EU is pitted against a no-deal contest, remain is slightly ahead, winning 52 per cent to 48 per cent, YouGov found.
It comes as Ms May was facing pressure to delay the so-called meaningful vote on Tuesday over the prospect of a devastating defeat at the hands of Tory rebels and her DUP allies.
Senior Conservative MP Sir Graham Brady, who chairs the backbench 1922 committee, said he would welcome the December 11 “meaningful vote” being deferred if no solution could be found to differences within the party over the backstop.
He told Newsnight: “I think the most important thing is to have clarity about how we might remove ourselves from a backstop… if we were to enter into one in the future.
“It’s having the answer to that question of substance that is most important, not the timing, so if that question can be answered in the course of the next few days then all well and good.
“If it can’t then I certainly would welcome the vote being deferred until such time as we can answer that question.”
Labour former prime minister Tony Blair also suggested it should be delayed as the PM was facing the prospect of “hitting a brick wall at speed”.
He said: “Personally, I don’t see what the point is in going down to a huge defeat.”
However Ms May has rejected pleas from cabinet ministers to defer the vote, saying: “What I am doing is leading up to a vote on Tuesday.”
:: YouGov collected data for this project from 27 November to 4 December from a sample of 20,910 respondents in Great Britain.
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.