The prime minister's decision not to risk such a high-profile contest had been widely expected but prompted taunts that Mr Blair is what the Tory leader dubbed "a real chicken".
Mr Kennedy said the prime minister was unwilling to debate without the "400 cheerleaders" who sit behind him in the Commons.
Mr Hague even urged the broadcasters to go ahead with the two proposed debates anyway. "If Tony Blair still refuses to show, we'll just leave an empty chair with a big sign of 'coward' for where Tony Blair would have sat if he'd had the guts to turn up," he said.
The televising of prime minister's questions in the Common, and the robust traditions of parliamentary and media debate in Britain, were used to justify Labour's refusal to take part in the American-style debates.
"The UK is not electing a president and our constitutional positions are entirely different," Mr Blair's official spokesman, Alastair Campbell, told reporters yesterday.
Mr Campbell had raised broadcasters' hopes in December, saying publicly that the idea was "perfectly good in principle" and that "my hunch is that at some stage it will happen".
But he and other senior advisers concluded this week that media obsession with election "process" - of which two TV debates would be an obsessive example - would only serve to detract from Labour's policy message.
"We want to concentrate on the issues which really matter to people," the Scottish secretary, John Reid, told Channel 4 News last night.
Peter Mandelson and Labour pollster Philip Gould are said to have backed the "withdrawal with dignity" strategy. Labour was determined to say yes or no before the campaign starts, probably in late March, to stop the issue being a distraction - as it was in 1997 when John Major made a desperate plea for a confrontation on TV.
Party officials and MPs engaged in campaign planning on all sides were therefore not surprised that Mr Blair would find an excuse. "There's not much in it for him," said one.
But the reasons given in a letter by Labour's communications director, ex-BBC journalist Lance Price, are those that have always existed.
"By comparison with other democracies, we have in the UK very lively political and media debate on a constant basis," he said.
Ministers will also be available to voters to discuss all the relevant issues outside "the Westminster village" in the election, he promised.
Blair aides denied that George W Bush's success in America - where he had been seen as the underdog but performed well in debates - was a factor.
The TV proposals had raised the prospect of legal challenges - demanding equal time or other restrictions - by smaller parties, notably the Scottish Nationalists.
When Mr Blair took part in a "meet the prime minister" session with voters in Leeds on ITV last month, the SNP successfully complained to the Independent Television Commission because a byelection was taking place in Falkirk at the time.
The BBC and ITV had buried their differences in favour of two debates - one chaired by David Dimbleby on the BBC, the other by his brother, Jonathan, on ITV. But despite Mr Kennedy and Mr Hague saying they would agree without condition, the January 31 deadline loomed without real negotiation taking place.
Mr Price explained: "Much is made of that fact that US presidential candidates hold TV debates. But we are not the US."
He pointed out that "when a sitting president is being challenged, his opponent is not known until a few months before the election. When a president is retiring, neither candidate is known until that time".
Citing the regular exchanges at question time, Mr Price added: "Over the course of a parliament these exchanges span many hours and cover many issues ... nothing comparable exists in the USA.
"Indeed, the recent Bush-Gore debate was the first substantive encounter between them. That cannot be said of the prime minister, William Hague and Charles Kennedy."