Prime Minister Gordon Brown has held the first meeting of his new Cabinet as one minister claimed the leadership issue has been "settled".

The immediate threat to Mr Brown's position receded after he faced down backbench critics at a make-or-break meeting in the House of Commons on Monday night.

Despite catastrophic results in European and council elections and a string of ministerial resignations, only a handful of MPs called for him to quit after a speech in which he admitted to "weaknesses" and promised a fresh approach and new policies.

In an attempt to draw a line under the failed efforts to oust the Prime Minister, Foreign Secretary David Miliband declared that even Home Secretary Alan Johnson, the "leading contender" to replace Mr Brown, is backing him "to the hilt".

But Mr Miliband dodged the question of whether he himself "flirted" with the idea of resignation after former Work and Pensions Secretary James Purnell's shock decision to quit the Cabinet last Thursday.

The Foreign Secretary said: "Flirtation is dangerous for married men, I'm not going to get into that."

Mr Purnell has insisted he stands by his call for Mr Brown to stand down to give Labour "a fighting chance" in the General Election expected next year.

Despite failing to trigger a walk-out of senior Cabinet ministers, he said he did not regret quitting, adding: "I said what I said, I stand by it."

On Wednesday, Mr Brown will seek to regain the political initiative by addressing MPs on his plans to clean up Parliament.

In the Commons, Mr Brown will update the House on progress towards the introduction of an independent regulator for Parliament in the wake of the scandal over MPs' expenses.

The move is designed to show Mr Brown has a forward-looking agenda on one of the key causes for voter disillusionment with politics.

Mr Miliband earlier said: "The Parliamentary Labour Party has reached a settled view about the leadership. The Labour Party does not want a new leader, there is no vacancy, there is no challenger.

"The leading contender, Alan Johnson, is backing the Prime Minister to the hilt. So that is that." He added: "I always believed that the right thing to do was to remain in the Cabinet.

"I was clear that the right thing to do was to make sure that all of my energies were dedicated to making sure there was a progressive, clear, strong Labour project at the next election."

Mr Brown has now completed a reshuffle of his administration without further resignations, and brought Shahid Malik back into his Government as a junior communities minister after the Dewsbury MP was cleared by an inquiry of irregularities relating to his housing arrangements.

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