Tony Blair conceded he would not serve a full third term yesterday, as backbenchers warned they were "sick and tired" of speculation about the Labour leadership.

In a meeting with Labour backbenchers last night, he said he would stand down in time for Gordon Brown, the Chancellor, to establish himself as leader before the next election.

Previously, the Prime Minister has always insisted he would continue in office for a f ull third term, which appeared to mean right up to the next election. But he refused to give in to demands to set a timetable for his departure.

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It was the first meeting between Mr Blair and back-benchers since last week's local elections, in which Labour lost 319 council seats and came third in terms of share of the vote, behind the Liberal Democrats.

West Midland Labour politicians last night expressed frustration at the continued uncertainty surrounding the leadership.

Sion Simon (Lab Erdington) said: "I want Blair and Brown to sort this out once and for all. This has got to stop."

However there was disagreement about whether Mr Blair should set out a timetable for resigning.

Khalid Mahmood (Lab Perry Barr) said: "Just by having given that deadline, it has raised expectations. But I don't think there should be a push towards saying he should go now."

Gisela Stuart (Lab Edgbaston) said: "We should focus on sorting out our schools and making the health service work.

"We need to get on with the manifesto we were elected on which, by the way, was with Tony Blair as Prime Minister."

And Rob Marris (Lab Wolverhampton South West) said: "I don't think we need a timetable at the moment, but we will need one eventually."

But Richard Burden (Lab Northfield) said: "There does need to be a timetable. If we know there is to be a new leader in place by the time of the next election then it is bound to cause debate, and we are at that point."

Speaking at a Downing Street press conference yesterday, Mr Blair said: "I will tell the Parliamentary Labour Party this evening that I have said we will have a stable and orderly transition to a new leader and I will see that this is done because it is in the interests of the country.

"But it is also in the interests of the country that in the meantime we get on with the job of governing."

He added: "I have said I will ensure an orderly and stable transition. I will do it in the time necessary for my successor to establish themselves."

However, he would not give in to demands to explain exactly when he would stand down, he said.