As the prime minister steps up efforts to sell her blueprint, a survey found that 46 per cent of people would prefer to remain in the bloc compared to 37 per cent who would choose Ms May's deal, if asked to pick in a new public vote.
The Survation poll, for the Daily Mail, also found that half of voters would opt to stay in the EU compared to 40 per cent who would support a no-deal, if those were the two options on the ballot paper.
Some 48 per cent would back offering the people a final say on the prime minister's Brexit deal - which The Independent is campaigning for - while around a third of voters (34 per cent) would oppose a fresh vote, the snap poll on Tuesday found.
Voters appear to have shifted towards Ms May's deal, with 37 per cent backing it, compared to 35 per cent opposing it. This compared to 27 per cent backing it and 49 per cent opposing it in a similar poll on November 15,
In a boost for the prime minister, some 41 per cent believe MPs should back the deal, while 38 per cent think they should vote it down.
It comes as the government was expected to publish stark economic analysis of the prime minister’s Brexit deal, as Ms May steps up her efforts to sell the blueprint to the public.
Whitehall officials have scrutinised the economic impact of Ms May’s deal and compared it to various scenarios, including staying in the EU or a Canada-style free trade deal - the Brexiteers’ preferred option.
The prime minister is likely to use to findings to persuade MPs to back her plan in a crunch Commons vote in two weeks time, where she is facing defeat at the hands of Tory rebels in both Brexiteer and pro-EU factions.
In a blitz of media interviews, Philip Hammond admitted that "in pure economic terms" the UK will be worse off under all possible Brexit outcomes.
Asked directly if the UK will be poorer under Mrs May's deal, Mr Hammond said: "The economy will be slightly smaller in the prime minister's preferred version of the future partnership."
The chancellor said analysis published today looks at the next 15 years, and shows the impact on the economy will be "very small", insisting it will still grow in that period.
But he told BBC Radio 4's Today programme: "I'm the Chancellor so of course I look at the economy as being of overriding importance, but there are other considerations.
"And I recognise that many people feel very strongly about the need to leave the European Union to regain control of our fishing waters, to regain control of migration and control of our borders, to have the right to do third-country trade deals.
"These are things which have value to people, and it is true that the economy will be very slightly smaller if we do the deal the way the Prime Minister has set out and negotiated, but the impact will be entirely manageable."
Asked if the UK would be better off staying in the EU, he agreed that remaining in the single market "purely on the economics" would give the country an advantage.
:: Survation interviewed 1030 people aged 18+ living in the UK online on 27 November
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