Theresa May's hopes of continuing as prime minister have been dealt a blow after a survey of Conservative supporters found 80 per cent think she should quit before the next general election.

A poll of readers of the ConservativeHome website found that more than a third (35 per cent) think the prime minister should resign immediately, while a further 45 per cent said she must step aside before the next election is due in 2022.

Just 19 per cent of respondents said Ms May should not resign at all.

The poll will come as blow to the prime minister on the eve of the Conservatives' annual conference, which kicks off on Sunday.

Although it found that Tory supporters were increasingly willing to give Ms May more time, with the proportion wanting her to resign immediately having fallen by 5 per cent since last month (down from 40 per cent), the number wanting her to quit before the next election is up 6 per cent (from 39 per cent).

The prime minister has come under mounting pressure over her Brexit strategy, which is deeply unpopular with many of her own MPs and party members.

She is expected to use the party conference in Birmingham to attempt to convince her party to back her Chequers plan, which she insists is the only alternative to a no-deal Brexit.

But Tory Brexiteers will try to force her to drop the strategy, which they say would keep the UK tied too closely to the EU.

Critics of the plan include Boris Johnson, the former foreign secretary, who used his latest newspaper article to once again savage the Chequers proposals.

Writing in The Telegraph, he said: "Overall, the Chequers proposals represent the intellectual error of believing that we can be half-in, half-out: that it is somehow safer and easier for large parts of our national life to remain governed by the EU even though we are no longer in the EU.

"They are in that sense a democratic disaster. There is nothing safe or 'pragmatic' in being bound by rules over which we have no say, interpreted by a federalist court.

"The Chequers proposals are the worst of both worlds. They are a moral and intellectual humiliation for this country. It is almost incredible that after two years this should be the opening bid of the British government."

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A number of other senior Conservative MPs also hit out at Ms May's leadership as she prepares for a conference that could determine her future as prime minister.

Former minister Robert Halfon said the Conservatives under her leadership were failing to provide "a proper Tory vision for the future".

Writing for ConservativeHome, he said: "We are stuck in the political rhetoric of the past, rather than providing a proper Tory vision for the future.

"It’s why even with ‘the most left wing leader in the history of mankind etc’, Corbyn’s Labour remains pretty high in the polls.

"They are speaking to the problems faced by many. We too often speak only for the few."

Sam Gyimah, a business minister, also voiced concerns, saying the Conservatives "have lost our way".

Writing for The House magazine, he said: "We can’t out-Corbyn Corbyn, and if we try we risk offering a pale imitation that leaves people yearning for the real thing.

“When I look at how we on the centre-right have reacted to the perceived failing of capitalism, I can’t help thinking we have lost our way."

Dominic Raab says Canada-style Brexit trade deal is 'off the table'

Mr Gyimah said his party was “confused about how to handle business” and had flip-flopped between “Trumpian economic nationalism” and “the old playbook, implying that if we simply deregulate and cut taxes, all will be fine".

Speaking to the same magazine, Mid Norfolk MP George Freeman, a former head of Ms May's policy unit, said the Tories risked becoming a "rump party of nostalgic nationalists".

He said: “This is a 1975, 1945, 1905 moment: when the underlying rules of our system of political economy profoundly change.

“A new generation of aspirational professional voters under 45 are rejecting the old model. Unless the Conservative Party reconnects with them, we risk becoming a rump party of nostalgic nationalists,”

Cabinet ministers also voiced fears over the Tories' prospects.

Liz Truss, the chief secretary to the Treasury, admitted she had been impressed with Labour's latest campaign video, which focused on "left behind" towns.