Research of almost 35,000 voters across 238 marginal seats projects a massive Tory landslide, with David Cameron commanding a majority of 146 as more than half of Labour MPs lose their seats.

The survey, carried out by YouGov for the PoliticsHome website and published in a Sunday newspaper, is reported to be the biggest such exercise in the key seats where the election will be decided. The results come as the Labour Party conference gets underway, and are particularly bad news for Brown, who hopes to use the gathering to relaunch his premiership.

If proved correct, it would see Labour reduced to just 160 MPs, its fewest since 1935, losing seats held since the First World War and being all but wiped out in the south of England.

Of more immediate concern to Brown are the findings from Glenrothes, where the SNP is predicted to win the looming by-election. A second humiliation north of the border following the Glasgow East loss to the SNP in July could prove fatal for Brown's leadership.

Those urging him to step aside will be encouraged by the finding that a third of potential Labour voters in the marginal seats would be more likely to vote for the party under a different leader.

Home Secretary Jacqui Smith would be one of eight Cabinet ministers booted out by the electorate should the poll be translated to a general election.

Transport Secretary Ruth Kelly, Skills Secretary John Denham, Defence Secretary Des Browne, Chief Whip Geoff Hoon, Justice Secretary Jack Straw, Work and Pensions Secretary James Purnell and Business Secretary John Hutton would also go, as well as a dozen other ministers and high-profile former Cabinet ministers such as Charles Clarke and Alan Milburn.

A total of 34,334 online interviews were carried out by YouGov between July 22 and August 4, and further fieldwork was carried out on September 18-19.

Earlier, Brown had brushed aside the rebellion against his leadership in contemptuous fashion, attempting to cast himself as the man best equipped to deal with the world's economic crisis.

In an opening address to the party's national conference in Manchester, the Prime Minister made only one oblique reference to the calls for his head, mentioning "the other stuff" that had taken place during last week's financial turmoil.

The challenge, which culminated in the resignation of Scotland Office minister David Cairns, threatened to overshadow the conference at one stage, but Brown quickly sought to show that events had moved on.

Referring back to the past few days, he said: "What a week! I don't think I've ever seen anything like it. Not the other stuff, but the world economy changing almost by the day and almost by the hour."

Brown was backed strongly by the conference hall yesterday as several delegates declared they wanted to see an end to the "unseemly squabbling" over the party leadership. The party begins four days of debate in Manchester, including a speech by new Scottish leader Iain Gray today and culminating in a leader's speech by Brown on Tuesday.

Replying to a question-and-answer session in which his leadership was raised, Brown said: "The eyes of the country are upon us, and the people of this country want us to address their concerns."

His strategists are hoping to capitalise on last week's crisis, claiming it was only the intervention by Brown and Chancellor Alistair Darling to allow the Lloyds TSB takeover of HBOS that held off a major banking collapse.

The theme is expected to be woven into his keynote speech. Many in the party say they are waiting to see how he performs before deciding whether he should lead the party into the next general election.

Brown also revealed that immediately after the conference ends he is to go to America, where he will press the case for global reform of financial regulations. This follows the Financial Services Authority's temporary ban on short-selling, announced last week.