Theresa May’s under-fire Brexit deal is the preferred option in only two parliamentary constituencies, while some 600 seats would support remaining in the EU first, a stark poll has shown.

The YouGov survey found that Tory-held constituencies, Broxbourne and Christchurch, were the only ones favouring Ms May’s blueprint, while 30 seats chose a no-deal Brexit as the best outcome.

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.

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 Ms May’s deal, no deal and remaining in the EU in order of preference, revealing 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 YouGov survey pointed to the fact that Ms May’s deal appears to suffer from being everyone’s second choice, failing to curry favour among either Remain or Leave voters.

The figures do change, however, when you look at results that would come through the alternative vote system, which allows people to put down a second preference.

In that instance, 276 seats would back remain, 176 would back Ms May’s deal and 180 would back no deal. Under a “condorcet” system which would see voters rank all options in order of preference, Ms May’s deal has the backing of 370 constituencies while remain has the backing of 262.

The poll comes as Ms May faced 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 11 December “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.

“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.”

Cabinet ministers resign over Brexit deal Show all 13 1 /13 Cabinet ministers resign over Brexit deal Cabinet ministers resign over Brexit deal Esther McVey Britain's Work and Pensions Secretary Esther McVey arrives to attend the weekly meeting of the cabinet at 10 Downing Street in London. - Britain's Work and Pensions Secretary Esther McVey resigned from the cabinet over draft Brexit deal AFP/Getty Cabinet ministers resign over Brexit deal Handout image taken from the Twitter feed of @EstherMcVey1 of the resignation letter addressed to Prime Minister Theresa May from Works and Pensions Secretary Esther McVey. PRESS ASSOCIATION Photo. Issue date: Thursday November 15, 2018. Ms McVey has resigned, saying the Brexit deal âdoes not honour the result of the referendumâ. See PA story POLITICS Brexit. Photo credit should read: @DominicRaab/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder. PA Cabinet ministers resign over Brexit deal Dominic Raab British Brexit Secretary Dominic Raab give a press conference at the end of the final round of talks in Brexit negotiations at the European Commission in Brussels, Belgium EPA Cabinet ministers resign over Brexit deal Handout image taken from the Twitter feed of @DominicRaab of the resignation letter addressed to Prime Minister Theresa May from Brexit Secretary Dominic Raab. PRESS ASSOCIATION Photo. Issue date: Thursday November 15, 2018. Mr Raab has resigned, saying he âcannot in good conscience support the terms proposed for our deal with the EUâ. See PA story POLITICS Brexit. Photo credit should read: @DominicRaab/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder. PA Cabinet ministers resign over Brexit deal Rehman Chrishti Vice Chairman of the Conservative Party Rehman Chrishti tendered his resignation letter this afternoon PA Cabinet ministers resign over Brexit deal Cabinet ministers resign over Brexit deal Anne-Marie Trevelyan Parliamentary private secretary in the Department of Education Anne-Marie Trevelyan resigned stating that she cannot support the deal Cabinet ministers resign over Brexit deal Handout image taken from the Twitter feed of @annietrev of the resignation letter addressed to Prime Minister Theresa May from Anne-Marie Trevelyan, a parliamentary private secretary in the Department for Education. PRESS ASSOCIATION Photo. Issue date: Thursday November 15, 2018. Ms Trevelyan has resigned saying she cannot support the Brexit deal after negotiations âbuilt on the UK trying to appease the EUâ. See PA story POLITICS Brexit. Photo credit should read: @annietrev/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder. PA Cabinet ministers resign over Brexit deal Sam Gyimah Universities minister Sam Gyimah resigned on November 30, claiming the government's decision to pull out of the EU's Galileo satellite navigation system as a deciding factor PA Cabinet ministers resign over Brexit deal Shailesh Vara Shailesh Vara who has quit as Minister of State for Northern Ireland, saying he cannot support Theresa May's Brexit agreement, which he said "leaves the UK in a halfway house with no time limit on when we will finally be a sovereign nation" PA Cabinet ministers resign over Brexit deal Cabinet ministers resign over Brexit deal Suella Braverman Brexit minister Suella Braverman has resigned, stating “It is not what the British people, or my constituents, voted for in 2016.” Cabinet ministers resign over Brexit deal Ranil Jayawardena Parliamentary private secretary to the ministry of justice Ranil Jayawardena resigned as he could not back the deal "in good conscience"

Former Labour prime minister Tony Blair also suggested the vote should be delayed as the PM is 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.”