Although deeply angry at Labour's aggressive campaign against the Liberal Democrat victor, Chris Davies, Mr Ashdown insisted that "of course parties co-operate, as we have done with the Conservatives and we are prepared to do with Labour. We have done so in local government."
John Major brushed aside the "disappointing" result which lost the Conservative Party the seat and left it in third place, but insisted that the Tories' showing of 24 percent demonstrated that "the bedrock of the Conservative vote stayed there more effectively in this by-election than it has done in the past."
While the Opposition celebrated the sixth successive Tory by-election loss in this Parliament, the style of the campaign and the closeness of Mr Davies's 1,993 majority provoked soul searching about the two parties' future relations.
Mr Ashdown, who just before the by-election tilted his party towards Labour by announcing for the first time that the Liberal Democrats would not prop up a minority Tory government, was clear the next move was up to Labour. "Part of a new politics that I believe in, and I understood Mr Blair believed in too, was the fact that we respect each others' parties and we respect our candidates. I leave you to decide whether that's been done but this is a matter for Labour to consider, not us."
Alan Beith, Liberal Democrat deputy leader, was more forthright. "Their campaign was extremely right-wing. They also very mischievously and misleadingly tried to target our candidate by saying he believed or said things he did not believe or say. It was pretty unpleasant sort of campaigning."
Labour said the Liberal Democrats had misled the electorate by saying from the outset Labour's challenge need not be taken seriously.
Senior Liberal Democrat strategists have made little effort to disguise their irritation with the style of the Labour campaign - managed by Peter Mandelson, MP for Hartlepool, but endorsed by the Labour leadership.
However, some argue privately that the ferocity of the contest will demonstrate to sceptical activists that Mr Ashdown's decision to end "equi-distance" between the two parties does not imply a new pre-election accord with Labour.
There were clear signs last night that some Liberal Democrat MPs - particularly in areas where the third party has historically offered alternative to the Tories - may seize on Labour's campaign to argue that the brakes should be put on further co-operation.
Mr Blair said last night on Channel Four News: "I don't think that [the by-election] is going to disturb sensible co-operation on issues between us." He said that the swing to Labour had been larger than that for the victorious Liberal Democrats and said there was clear evidence that Tory voters were now defecting straight to Labour.
Mr Mandelson, Labour's campaign manager, insisted Labour is "still open to dialogue between the two parties" but that this did not mean that the party would not fight as hard as it could for every vote. One Labour strategist said: "We can talk about future co-operation but we will do so from a position of strength."
Mr Major said the result was disappointing and described it as "a typical mid-term by-election result". Insisting his parliamentary majority, down to single figures, was "entirely workable", he added: "You've seen by- election results like this in Parliament after Parliament ... But the factor that is always consistent with these defeats is that we win them back at the general election, and I've no doubt that will happen on this occasion."
By-election reaction, page 2
Mandelson profile, page 17