Alan Johnson would deny David Cameron an overall majority at the next general election if Labour ditched Gordon Brown and installed him as prime minister, according to a new poll for The Independent.

The ComRes survey provides the first evidence that a change of leader could dramatically transform Labour's prospects. The findings were described as "stunning" by rebel Labour MPs last night. They believe it could influence Labour's agonised debate over whether it should back or sack the beleaguered Prime Minister.

Under Mr Brown's leadership, the Conservative Party would win an overall majority of 74, according to ComRes. But if Mr Johnson, the Home Secretary, replaced Mr Brown, the Tories would be six seats short of a majority in a hung parliament – raising the prospect of a deal between Labour and the Liberal Democrats to keep the Tories out. Mr Johnson is the only one of eight possible Labour leaders who could prevent an outright Tory victory. Under Jack Straw, David Miliband, Jon Cruddas, Ed Balls, Harriet Harman, James Purnell or Mr Brown, Mr Cameron would win a majority of between 10 and 94, ComRes found. Significantly, Labour would do better under Mr Straw, Mr Miliband, Mr Cruddas and Mr Balls than under Mr Brown.

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Mr Johnson is also the most popular of the eight contenders among people who regard themselves as natural Labour supporters and among people who backed the party at the last general election. Charles Clarke, who called on the Prime Minister to stand down at a packed meeting of the Parliamentary Labour Party (PLP) last night, said of the ComRes survey: "This poll is the convincing evidence that Labour needs a serious and considered debate about its future direction and leadership."

Labour MPs recalled that similar polls, suggesting that a change of leader would revive Tory fortunes, contributed to Margaret Thatcher's ousting by her backbenchers and ministers in 1990. Mr Brown was cheered as he arrived at what had been billed as a meeting that could decide his fate. There was unusually candid criticism during the heated 90-minute session as three former ministers – Fiona McTaggart, Tom Harris and Mr Clarke – told him to his face the fact that he should stand down. Siobhain McDonagh, a former whip, also called on Mr Brown to go.

The Prime Minister won the backing of most of those present. Striking a note of humility, he told the meeting: "I have my strengths and I have my weaknesses. I know I do some things well and some things I don't do well. But I've learnt that I have to keep listening all the time."

Mr Brown promised to consult more widely inside his party, run a more collective leadership and to be more open and transparent in the way he ran Downing Street. He pledged to be a full-time Labour leader as well as a full-time Prime Minister.

Dismissing calls for his resignation, he said: "You solve the problem not by walking away but by facing it, doing something about it." He warned that previous Labour governments had been brought down by a combination of economic problems and party disunity. He insisted there were no huge ideological differences within the party, telling the meeting: "There isn't a resignation letter I have seen that mentions policy differences."

He insisted he was not begging for unity but was "making an argument for unity", adding: "I am here because of what I am and what I can offer to this progressive age because I know what needs to be done."

A string of Labour grandees, led by the former leader Lord Kinnock, rallied support behind the Prime Minister. He warned that divisions equalled the "death penalty" in politics.

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David Blunkett, the former Home Secretary, told the rebels they had 24 hours to "put up or shut up," warning: "We cannot take this blood-letting any longer."

Brown allies said afterwards they were confident he would survive and claimed the plot to unseat him was fizzling out. Some potential rebels admitted it might be put on hold until the autumn, despite Labour's disastrous performance in the European elections, in which it came third behind Ukip after winning on a historic low 15 per cent of the vote.

The Prime Minister's attempt to steady the ship ran into more problems when Jane Kennedy, an Environment minister, refused to serve in his administration. She accused Mr Brown of sanctioning smear campaigns against Labour politicians and the undermining of his critics.

Stephen Byers, the Blairite former cabinet minister told the meeting staged by the modernisers group Progress last night: "We need a leader who regards Labour Party members as assets to be valued. A leader who sees Labour MPs as colleagues to be worked with and not threats to be briefed against... A leader who is decisive and not timid. Who can inspire and take our country through these difficult times. We need a leader who can win for Labour at the next general election and not take us to a humiliating defeat. Gordon Brown is not that leader."

Mr Byers added: "Gordon Brown knows who will pay the real price of a Labour defeat. So for those people, families and communities who need a Labour government to protect and promote their interests, Gordon Brown should stand down now as Labour leader and Prime Minister."

Frank Field, another former minister, said: "Labour cannot win with the present Prime Minister. I was one of the seven who would not support his coronation after Tony Blair was shoehorned out of No 10. But even I didn't think a Brown administration would be as inept as this one."

The ComRes poll puts the Tories on 38 per cent (up eight points since its last survey a week earlier), Labour on 22 per cent (no change), the Liberal Democrats on 20 per cent (up two points) and other parties on 20 per cent (down 10 points).

The C2 skilled manual workers and people in the bottom DE social group are twice as likely to vote Tory than Labour, confirming that Mr Brown's party has suffered disproportionately from the scandal over MPs' expenses.

The Tories retain the support of 88 per cent of those who voted for them at the 2005 general election, while 63 per cent of Labour voters would back the party in an election now. So would 74 per cent of those who endorsed the Liberal Democrats.

Last night, some Brown critics acknowledged that the rebellion was fading. One left-winger said: "He has probably done enough. The idea of an early general election is terrifying colleagues."

One leading rebel said: "I'm pretty pessimistic. I think Gordon's going to survive, but discontent will rumble on. There will be simmering disharmony. That is the worst possible scenario for the Labour Party.

"My gut instinct tells me that the carrots and severe sticks from No 10 and the whips have persuaded people to move over. People are being threatened with being smeared in the tabloids if they didn't fall into line."

ComRes telephoned 1,001 GB adults between June 5-7, 2009. Data were weighted by past vote recall. ComRes is a member of the British Polling Council and abides by its rules.

Independent poll: Which leader would put the smile back on Labour's face?

Alan Johnson, Home Secretary

Man most likely to succeed Gordon Brown if he is toppled before general election.

Election result with him as leader:

Con 36% Labour 26% Lib Dems 19% (Con six seats short of majority.)

Support among Labour identifiers: 76%

Jack Straw, Justice Secretary

His withdrawal of support could finish Brown.

Election result with him as leader:

Con 36% Labour 25% Lib Dems 19% (Con majority of 10)

Support among Labour identifiers: 71 per cent

David Miliband, Foreign Secretary

Raised profile last summer but campaign faltered

Election result with him as leader:

Con 37% Labour 25% Lib Dems 19% (Con majority: 30)

Support among Labour identifiers: 73%

Jon Cruddas, Backbencher

Turned down ministerial job and enjoys support on left of party.

Election result with him as leader:

Con 36% Labour 22% Lib Dems 21% (Con majority of 42.)

Support among Labour identifiers: 69 per cent

Ed Balls, Schools Secretary

Brown's favoured successor. Ambition to become Chancellor.

Election result with him as leader:

Con 37% Labour 23% Lib Dems 20% (Con majority of 46)

Support among Labour identifiers: 67 per cent

Gordon Brown, Prime Minister

Hoping to see off plotters as Cabinet did not join revolt

Election result with him as leader:

Con 38% Labour 22% Lib Dems 20% (Con majority: 74)

Support among Labour identifiers: 71 per cent

Harriet Harman, Deputy leader

Would be strong candidate in full-scale leadership contest.

Election result with her as leader:

Con 38% Labour 22% Lib Dems 20% (Con majority of 74)

Support among Labour identifiers: 67 per cent

James Purnell, Former cabinet minister

Blairite who quit as Work and Pensions Secretary last Thursday. Would win respect if Brown was ousted.

Election result with him as leader:

Con 38% Labour 21% Lib Dems 21% (Con majority of 94)

Support among Labour identifiers: 66 per cent