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Gordon Brown is to slow down the part-sale of Royal Mail and announce an Iraq war inquiry within days as he tries to prevent dismal European election results strengthening the bid to oust him.

The Prime Minister appeared today to be seeing off his critics, with Labour MPs clearly hesitant to sign an e-mail calling on him to quit. The threat from the Cabinet appeared to have gone, as ministers and MPs accepted that Mr Brown’s demise would inevitably mean an early general election.

But Downing Street remains nervous over the impact of the election results, which see Labour in danger of being forced into fourth place behind the Conservatives, Liberal Democrats and UKIP.

A meeting of the Parliamentary Labour Party tomorrow will be crucial to Mr Brown’s short-term future.

All the signs during today were that it could be the rebels rather than Mr Brown who would be in the firing line. He received a boost when Jon Cruddas, the leading leftwinger, said it would be “madness” to think that Labour’s problems could be solved by throwing Mr Brown overboard.

Looking much more relaxed than he has recently, Mr Brown got a warm reception from party members who turned their anger on dissident Labour MPs rather than him. The hastily convened meeting, and its televising, was clearly designed to send a message to the PLP gathering.

Mr Brown said that the public would not understand if the Government gave up at a time when it was faced with the problems of tackling the recession and cleaning up Parliament.

“What would they think of us if ever we walked away from them at a time of need? We are sticking with them,” he said.

“We have a purpose, we have a mission, we have a task ahead. We are going to get on with that task of building a better Britain.”

To appease Labour MPs further, Mr Brown is soon to give the go-ahead for the long-awaited Iraq war inquiry. Sources said he was “reflecting” on its timing and has asked the Cabinet Secretary Sir Gus O’Donnell to advise him on terms of reference, membership and timing. Mr Brown will say something this week.

Also, Lord Mandelson appears to be ready to go some way to placate doezens of Labour MPs who oppose his plans to part-privatise the Royal Mail. While continuing to insist the move is necessary to safeguard the business’s future, he is expected to concede that the time is not right commercially at present to go ahead with the sale to an outside interest. Labour MPs will ask for that to be accompanied with a promsie to delay the legislation as well.

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