The backbenchers, many speaking publicly for the first time, have been moved to hasten Blair’s departure after his majority was slashed by 94 in Thursday’s general election.

Many of them say they were shocked by the hostility shown towards them and the prime minister on the doorstep during the election campaign. With a smaller majority, backbenchers will wield far more power and have the potential to help vote down key government bills in the forthcoming Queen’s speech, including soon-to-be-published legislation on ID cards.

Further pressure has been put on Blair to go early, despite his stated intention to serve a full third term, by Michael Howard’s announcement that he is quitting as leader of the Conservatives. Howard told friends that one of the reasons for his statement on Friday was to raise the pressure on Blair to make an early exit himself.

Some MPs close to Gordon Brown believe Blair may decide to quit this year, using the G8 summit in Gleneagles in July or the party conference in autumn to stage an early exit.

Downing Street sought to play up the election result by reminding MPs Labour had never won three successive terms in office, that Thursday’s majority was bigger than that won by Margaret Thatcher in 1979, and that Howard’s Tories had won fewer seats than Michael Foot in 1983.

A Blair aide played down the threat from Labour rebels: “Everyone knows that when you have a large majority people feel more comfortable rebelling against the government, but when you don’t have one, people don’t.”

However, the comments by MPs this weekend suggest No 10’s hopes may not be realised, particularly if Blair continues to commit himself to serving a full term. At least 30 of the 100 MPs contacted by The Sunday Times wanted Blair to go sooner rather later, many within a year. It follows an article by Robin Cook, the former foreign secretary, in which he called on Blair to step down early, even before the local elections next year.

The prime minister will this week seek to shore up support among his MPs when he addresses a meeting of the parliamentary Labour party at the House of Commons.

But yesterday Frank Dobson, the former health secretary, described Blair as an “electoral liability” who would have to go sooner rather than later.

He suggested that if Britain scrapped plans for a referendum on the European Union constitution after a French no vote at the end of this month, many MPs believed he could go even quicker. “Lots of people said on the doorstep during the campaign they couldn’t vote Labour because of Iraq but an even larger proportion said they wouldn’t vote Labour again until Tony Blair had gone. And that’s a major problem.”

John Austin, MP for Erith and Thamesmead, said Blair should go before the party conference. “He was a liability and not an asset in this election. You can’t beat about the bush. Blair was a negative factor on the doorstep, time and time and time again,” he said. “We need a mechanism like the Tories where the grandees go round and tell the leader it is time for him to go. I think it was somewhat arrogant to say he was going to continue with a full term.”

Ian Davidson, MP for Glasgow South West and one of the few candidates to benefit from a swing to Labour, said the perfect time for “regime change” was the referendum on the EU constitution next year. “It needs to happen sooner rather than later,” he said.

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