Mr Blair's hopes of an early announcement of the Government's plans have been scuppered by a tough rearguard action by Mr Straw, who is reluctant to introduce legislation on the controversial issue.
Labour MPs said yesterday that Mr Blair's hands had been strengthened by the party's strong performance in Thursday's by-election in Eddisbury, Cheshire, where Labour came a close second to the Tories in a contest dominated by the Prime Minister's promise to outlaw hunting before the next general election.
Only two weeks ago, Downing Street said specific proposals would be issued before MPs leave for their summer recess next Tuesday. But the row between Mr Blair and Mr Straw has put that in grave doubt, and the Government may now merely issue a statement promising detailed proposals in the autumn.
"Jack Straw is a formidable fighter, but in a battle between his doubts and Tony Blair's credibility, Tony will win," said one insider. He said there would be uproar among Labour MPs if Mr Blair retreated from his recent promise.
Hilary Armstrong, the local government minister, cast fresh doubt on the Government's commitment yesterday, when she said that a Bill might not be drafted in time for the Queen's Speech in November. But Mr Blair's spokesman insisted: "There has been no change of tack at all. The Prime Minister has been clear about taking it forward, and taken forward it will be."
Mr Blair is believed to want legislation this autumn, so the issue does not dominate Parliament in the run-up to the general election. A possible compromise between him and Mr Straw is for the Government to make parliamentary time available for a Private Member's Bill rather than bring in its own legislation.
Yesterday both Mr Blair and Mr Hague claimed a success in the Eddisbury by-election, a once-safe Tory seat, where the Tories' 1,606 majority was only 421 higher than at the 1997 general election.
Although the Tories were relieved to win, the result failed to keep up the momentum of Mr Hague's triumph in last month's European elections. If Thursday's result were repeated at the next general election, the Tories would win only an extra 12 seats, leaving Labour with a massive Commons majority.
Mr Blair said: "It is an amazing result. For the Conservative Party not to advance on their general election position when we are in mid-term government is a brilliant result. If we had had another week we could have won it."
But Mr Hague insisted: "We are obviously very pleased with the Eddisbury result, to increase our majority in any election is obviously a very good thing.
"The Labour Party really put everything into this campaign, Tony Blair included, they went flat out to win this election and we defeated them," he said.
The Tory leader accused Labour of "shameless exploitation" of the hunting issue during the campaign, following a "cynical and opportunistic" pledge by Mr Blair. But Labour officials insisted the proposed ban had proved popular, enabling the party to mobilise its activists and voters in the by-election.
The contest was triggered by the appointment of Sir Alastair Goodlad, the former Tory MP, as Britain's High Commissioner to Australia.
Stephen O'Brien (C) 15,465 (44.83%, +2.31% on 1997 general election)
Margaret Hanson (Lab) 13,859 (40.17%, +0.04%)
Paul Roberts (LD) 4,757 (13.79%, +0.56%)
Alan Hope (Loony) 238 (0.69%)
Roger Everest (Ind Euro C) 98 (0.28%)
Dinah Grice (NLP) 80 (0.23%)
C maj 1,606 (4.66%)
1.13% swing Lab to C
Electorate 67,086; Turnout 34,497 (51.42%, -24.36%)Reuse content