Gordon Brown's first anniversary as prime minister was marked in appropriately macabre style on Friday, with Labour MPs claiming to feel suicidal or physically ill after the party finished a humiliating fifth in the Henley by-election.

Just when Mr Brown's advisers believed Labour's collapsing fortunes might have bottomed out, the party drilled further into the political bedrock by securing even fewer votes in Henley than the Greens and far-right British National party.

It was the first post-war British by-election where a governing party has finished fifth and the first time Labour has ever finished behind the BNP or its predecessor parties. Labour also lost its deposit, securing just 3 per cent of the vote.

Mr Brown faced renewed personal criticism, with one Labour MP labelling him "a loser" and another urging him to stand down in the interests of the party and his own health.

Labour MPs felt a particular horror at the party failing to beat the BNP in a parliamentary by-election. Stephen Pound, MP for Ealing North, said: "My first reaction was to head to the library with a glass of whisky and a revolver." Tessa Jowell, Olympics minister, said she "felt sick".

The Conservatives comfortably held Henley - a seat vacated by Boris Johnson, the new London mayor - with a majority of over 10,000 and 57 per cent of the vote. The Liberal Democrats finished a disappointingly distant second.

David Cameron said the result showed the Tories were picking up votes from the Lib Dems - a rare event in a by-election - but said it was "disastrous" for Labour. The prime minister shrugged off the result: "By-elections come and by-elections go," he said.

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But Lord Levy, Labour's former chief fundraiser, said Labour should "seriously consider" ditching the prime minister, and Ronnie Campbell, Labour MP for Blyth Valley, quoted in the Evening Standard, said: "I don't like to back losers and he's a loser at the minute."

Meanwhile, David Drew, Labour MP for Stroud, said: "There's no point doing the job when you are not enjoying it and it's all too hard. He's got to look at himself. He's got to make that decision."

The Labour campaign was all but invisible in Henley. As the Lib Dems and Conservatives rallied troops for a long fight as soon as Mr Johnson was elected mayor, Labour officials concentrated on lowering the expectation bar.

With a note of gallows humour, these officials quipped that it would be a triumph for Labour to hold on to its £500 deposit.

This despondency was matched by an unwillingness to devote resources to the campaign or to throw waves of cabinet ministers into the fray. Labour strategists feared that if they raised the profile of the campaign, the humiliation of a poor result would be compounded.

Downing Street officials claim the party barely spent £10,000 on the by-election campaign, while visiting cabinet ministers were thin on the ground. That lack of effort was laid bare when the votes were counted.

For the Lib Dems, a party that draws much of its pride from its outsized performances at by-elections, the result was a big disappointment. At times the campaign did misfire, selecting a candidate with dubious local ties and misrepresenting some data about schools.

But activists have began asking more fundamental questions over whether the tactics that had served them so well in the past were still as potent against a resurgent Conservative party.

It prompts a national debate over whether Nick Clegg, the party's newly blooded leader, should focus on picking up disillusioned Labour voters rather than finding a soft Tory underbelly in the south-east.