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 strong poll has shown.

The YouGov survey found that Tory-held constituencies, Broxbourne and Christchurch, were the only ones favoring 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 with the MPs and the public,

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 an order of preference, revealing the overwhelming majority of constituencies.

Staying in the EU gains 46 per cent of national support, while Ms May's deal and no deal were on 27 per cent, the poll found.

Ms. May's deal appears to be second to none, failing to curry favor among either Remain or Leave voters.

The figures do change, however, when you look at the results.

In that instance, 276 seats would be back, 176 would back Ms May's deal and 180 would back no deal. Under a 'condorcet' system which would see all the options in order of preference, May's deal has the backing of 370 constituencies.

The poll comes as Ms May faced pressure to delay the so-called meaningful vote on Tuesday of 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.

He told Newsnight: "I think the most important thing is to have clarity about how we could make a backstop.

Then it's all good and good.

"If it can not then I would certainly welcome the vote being deferred."

Former Labor prime minister Tony Blair, therefore, suggested the vote should be delayed as the PM faces the prospect of "hitting a brick wall at speed".

He said, "Personally, I do not see what the point is going down to a huge defeat."

However, Ms May has rejected pleas from cabinet ministers to defer the vote, saying: "What I'm doing is on Tuesday."

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