Both the Tories and the Liberal Democrats saw their share of the vote rise compared with the 2005 General Election while Labour's fell by more than 11%.
The by-election was triggered by Mr Johnson's resignation after he was elected mayor of London.
Speaking on Friday, Mr Cameron said: "It's an absolutely excellent result in Henley" but a "disastrous result for the Labour Party".
And he said he believed it was "the first time in a long time when there's been a contest between the Conservatives and Liberal Democrats where there's been a swing to the Conservatives."
"I think what we saw was people who voted for all sorts of different parties, including the Liberal Democrats, now looking at the Conservatives and saying: 'Yes this is an alternative government that I can believe in'."
Oxfordshire councillor Mr Howell said the vote showed that people had had enough of Labour: "It's clear that the New Labour coalition is falling apart and that the Conservatives under David Cameron's leadership are on the march."
Health Minister Ben Bradshaw admitted it was a "terrible result" for Labour but said it was down to current economic conditions rather than the unpopularity of Gordon Brown.
He told BBC Radio 4's Today programme: "When people start feeling the pinch and start feeling a reduction in their disposable income ... they take their anxiety out on the government.
"I don't believe he is personally unpopular," he added, saying that it was the "completely irrational" criticism by political commentators that was fuelling negative perceptions.
The Liberal Democrat candidate, Stephen Kearney, said voters were angry and fed up with the government.
"This is an abysmal result for the Labour party that has been in government for almost 11 years and has lost most of its support.
"But I have found no positive enthusiasm for the Conservative alternative.
"The Conservatives can say what they are against, but they have failed to say anything about what they are for and what they stand for."
And Lib Dem leader Nick Clegg said the result showed Mr Brown's days in No 10 were numbered.
"Labour's days are well and truly over and it is the Liberal Democrats who are challenging the Conservatives in the south and Labour in the north," he said.
Meanwhile, a YouGov opinion poll for the Daily Telegraph suggests Labour has closed the gap on the Tories over the past month.
Labour was up five points on the month at 28% - still 18 points behind the Conservatives who dropped one point to 46%. The Liberal Democrats were down three on 15%.
But 61% of those surveyed thought Gordon Brown was a liability to the party, compared to 21% when he came to power a year ago.
Last year, 62% thought Labour would win the next general election, but that has dropped to 16% while 67% now think that the Conservatives are on course for victory, the poll suggests.
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