Labour would gain 93 seats from the Conservatives to become the next government if a general election were held now, according to a poll of marginal constituencies.

Labour would gain 109 seats in total, taking them to 367 MPs and giving them a majority of 84, the research found.

The survey, carried out by the Conservative donor Lord Ashcroft, found there would be an 8% swing to the opposition in the most closely contested seats.

It comes amid claims that a canvass of Tory activists found just 7% believed the prime minister, David Cameron, will secure victory in 2015 and is likely to increase unease among already unsettled party members.

Nearly 20,000 voters in 213 constituencies were polled for the study, which found that Labour would win 93 of the 109 most marginal Tory seats, with the biggest swing to the opposition in the Thames estuary and Midlands.

Based on the research, the Liberal Democrats would lose 17 constituencies in England and Wales to their coalition colleagues and 13 to Labour.

Lord Ashcroft announced the findings on Saturday at the Victory 2015 conference being staged by the website Conservative Home.

He said: "I don't want to see a Labour majority of four, let alone 84, but I hope this puts the challenge into some sort of perspective. We have a long way to go to hold onto the seats we gained last time, let alone pick up many more. But things are slightly less grim than the headline polls suggest, and we have everything to play for."

The Tory planning minister, Nick Boles, said on Friday night that the party had "screwed up" in the Eastleigh byelection but warned that it must not swing to the right after the drubbing.

He suggested the party had failed to offer voters any hope and had repeated the same mistakes it has been making for more than a decade.

The Times reported that it had seen details of a poll of Tory supporters that showed just 7% believed Cameron will win an overall majority at the next general election, while three-quarters expect Labour to be in power.

Boles told the Times that last week's Hampshire by-election, which saw the Tories pushed into third place behind Ukip, had been a "truly rotten campaign".

He said: "Where was the hope? It was as if modernisation had never happened.

"We screwed it up. We didn't even screw up in a new way. We screwed it up in an old way that we have been doing for a decade. It's so frustrating."

But Boles, an ally of the prime minister, warned plotters they needed "their head seeing to" if they believed it was wise to attempt to oust Cameron.