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Theresa May faces an uphill task to sell her Brexit plan after a poll shows it has been given the thumbs down by voters.

The survey by Deltapoll reveals most people do not believe the Prime Minsister’s claim to have delivered a good deal.

And a majority of those polled disagree with Mrs May’s assertion the agreement is in the national interest and delivers on the result of the referendum.

Asked if the Prime Minister was accurate to say “it was a good deal”, 53% say the claim is false and 30% say it is true.

Voters also reject her claim it was on the only deal available, with 45% saying she is wrong to state this and 42% saying she is right.

(Image: AFP/Getty Images)

Downing Street will also be alarmed that Mrs May’s promise the withdrawal agreement will end freedom of movement is also disputed by the public.

According to Deltapoll, only 39% believe it will stop migration from the EU, with nearly half (47%) saying the Prime Minister is wrong to make such a claim.

Asked if Mrs May was right to say the “deal is in the national interest”, 49% said it is false and 37% say it is true.

Voters are also sceptical about her claim the agreement honours the result of the 2016 referendum with 47% disagreeing with the PM and 38% agreeing.

A narrow majority, 46% to 41%, also say the PM is wrong to claim the deal means we "take back control."

The findings are a further blow to the Prime Minister as she tries to convince MPs to back the withdrawal agreement in the crucial vote on 11 December.

Unless there is a major shift of opinion she is facing for near certain defeat.

Up to 100 Tory and DUP have indicated they could vote down the deal.

The majority of Labour MPs, 11 Lib Dems and the 35-strong SNP will also vote against.

Mrs May has tried to reach out over the heads of MPs by touring the country this week to drum up support for her plan.

But the poll shows that a majority of voters disbelieve her main claims.