Boris Johnson‘s pledge to use the election to “get Brexit done” is failing to convince voters, according to a new poll which shows the majority think a Christmas poll will not resolve the deadlock.

Less than a third of people (29 per cent) believe an election will break the Brexit logjam, compared with an overwhelming 56 per cent who believe a new parliament is unlikely to make progress.

The exclusive survey by BMG Research also reveals that a majority would rather stay in the EU than leave with the prime minister’s deal if offered the choice in a Final Say referendum.

When asked to pick between Mr Johnson’s Brexit blueprint and staying in the EU, 41 per cent opted to remain, while 35 per cent backed the deal. Some 25 per cent did not know or would not vote.

If offered a straight choice on the ballot paper between revoking Article 50 and leaving without a deal, voters picked scrapping Brexit by 42 per cent to 35 per cent.

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However, the prime minister’s deal won out (33 per cent) when pitted against no deal (20 per cent). In this scenario, the majority of people did not know or would not vote (47 per cent).

As the election campaign got underway in earnest, the prime minister’s “people vs parliament” message appeared to be gaining traction with voters.

The survey, conducted between 5 and 8 November, found 71 per cent of people believed MPs were responsible for preventing Brexit from taking place on 31 October, compared with 19 per cent who thought parliamentarians were not at fault.

When asked the same question about the parties, 58 per cent blamed Jeremy Corbyn and Labour, while 26 per cent said they were not responsible.

Mr Johnson was blamed by 49 per cent, compared with 37 per cent who thought he was not at fault.

The Tories got off to a difficult start on the election trail, following the resignation of Welsh secretary Alun Cairns over his knowledge of his former aide’s involvement in the collapse of a rape trial.

Jacob Rees-Mogg, the leading Brexiteer, was also forced to apologise for saying it was “common sense” for residents to flee the Grenfell Tower fire.

Despite the controversies, the BMG poll shows the Tories gaining ground with 37 per cent, compared with 31 per cent before the election was called.

Labour was on 29 per cent, up from 26 per cent in October, while the Liberal Democrats have fallen to 16 per cent, down four points from the previous month.

The Brexit Party also appears to be losing ground from 11 per cent in October to 9 per cent this month.

Rob Struthers, head of polling at BMG, said: “Findings from our first vote intention poll of the 2019 general election campaign suggest that support for Labour and the Conservatives has increased at the expense of the Liberal Democrats and the Brexit Party.

“Perhaps a product of media coverage so far, or the first-past-the-post system beginning to focus minds, this poll presents some early warning signs for the two main challengers to two-party dominance at this election.

“Fielded during the first days of the campaign, findings from this poll represent the highest vote shares we have seen for both main parties for some time.

“Corbyn’s Labour Party last recorded a higher share of the vote in May of this year. In the case of Johnson’s Conservatives, we have to go as far back as March of this year to find a month where we found their support at this level or above.

“Meanwhile, the Liberal Democrats and the Brexit Party, who would have been hoping their strong stances on Brexit will galvanise support during this campaign, both see their vote shares squeezed.”

It comes as two new tactical voting sites were launched by both campaigner Gina Miller and the People’s Vote group, which aim to advise voters how to prevent Mr Johnson’s gaining a majority for Brexit.

Best for Britain, another anti-Brexit campaign, launched a site at the end of October, which sparked a row over its recommendation of Liberal Democrat candidates in some Tory/Labour marginals.