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"It was in many ways the end of New Labour. I think it was a great mistake," Mr Cameron said of the class-based campaign.
Mr Timpson, 34, is a barrister but his father heads the Timpson chain of shoe-repair and key-cutting shops.
George Osborne, the Shadow Chancellor, said that Labour had resorted to "personal class war attacks" and "dog whistle" politics on immigration in a desperate attempt to avoid another devastating reverse after their drubbing in the May 1 local elections.
"Labour under Gordon Brown has abandoned the centre ground," he told BBC Radio 4’s Today programme. "There is a new ’nasty party’ in British politics and it is the Labour Party."
Harriet Harman, the Labour deputy leader, accepted that it had been a bad result for Labour but said that it did not mean that the Tories were on course for victory at the next general election.
And while she acknowledged that there were "discordant voices" within the party, she rejected suggestions that there could now be moves among Labour MPs to replace Mr Brown as party leader.
"I don’t think that will happen," she told Today. "The overwhelming majority of people in the Labour Party - and I speak to constituency chairs up and down the country in my capacity as deputy leader - are solidly behind Gordon Brown and what he stands for, which is a strong economy and fair society. He is the man with the experience to make sure that happens."
But the Labour leftwinger John McDonnell, who challenged Mr Brown for the leadership last year, warned the party that it must change.
"Things are just going from bad to worse for the Government. It would be an immense misreading of the situation for New Labour ministers to dismiss this result as simply mid-term blues," he said.
"The Prime Minister’s re-launch after the disaster of the local election results has proved to be totally ineffective. This result demonstrates the overwhelming anger and contempt in which New Labour is now held by our traditional supporters. The lesson tonight for the Labour Party is that it is change or bust."
The Conservatives' next electoral challenge is likely to come in more natural Tory territory: the south Oxfordshire seat of Henley, currently held by Boris Johnson, who promised to resign it during his successful campaign for the London mayoralty.
Capitalising on the Crewe result, the party is expected to move the writ setting a by-election in motion the week after next, for a vote on either June 26, or, Henley Regatta permitting, July 3.
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