Ministers expect a Cabinet reshuffle at the end of next week as Gordon Brown seeks to reassert his diminishing authority, The Times has been told.

Mr Brown will appeal over the heads of mutinous MPs to activists and voters tomorrow with a highly personal speech to Labour’s conference in Manchester. In revealing more of his background and personality, he hopes to reintroduce himself to the British public, senior allies say.

The Prime Minister is to make an impassioned appeal for more time to steer both the country and his party through the economic downturn, emphasising his experience of previous world financial crises.

In an interview yesterday he admitted that he had made mistakes but insisted that he would not “bail out” in the face of pressure. “Of course I always want to do better and I will do better,” he said.

Cabinet ministers expect the Prime Minister to continue his political fightback with a purge of his critics before MPs return to Parliament.

Although the resignations of two ministers failed to trigger a mass revolt before the party’s gathering in Manchester, they exposed Mr Brown’s weakness when Cabinet ministers refused to condemn the rebels.

Senior ministers inflicted more humiliation on their leader last week by leaking a damaging account of a Cabinet meeting last Tuesday. Mr Brown is being urged by his close allies to sack those suspected of disloyalty.

Supporters acknowledge, however, that he has limited room for manoeuvre and dare not risk sacking leading Blairites such as John Hutton for fear of triggering a full-scale leadership challenge. Some ministers believe that No 10 is encouraging speculation over a reshuffle in an attempt to keep critics in line.

David Miliband, the front-runner to take over as leader, maintained a high profile during the first full day of the conference but sought to avoid direct public criticism of the incumbent. The Foreign Secretary insisted that Labour had to be honest about what it had got wrong if it was to engage with voters.

At a fringe meeting, he also gave warning of a “sense of fatalism” in the party that had to be tackled.

Addressing a Progress rally later, Mr Miliband went further, issuing what amounted to a rallying cry to his supporters. “We have people coming though in their twenties and thirties who are going to carry the party forward. And our responsibility as those people have risen into positions of influence in the party now is that we never say that we worked so hard to get this far but now we are willing to step back. The point of working this hard to get this far is not to let it go.”

Another likely leadership candidate, Jon Cruddas, set out proposals to introduce a 45 per cent top rate of tax. The backbench MP, who is supported by the unions, said that the party had to find the “guts” that produced its 1997 election result.

“What has happened over the last week is symptomatic of the fact that we do need new remedies, new proposals, new ideas to put in the mix,” he told the Sunday Live programme on Sky News. “There is an argument for having a higher top rate — say on those over £175,000 a year — and using that money to remove all of those who have nudged into the higher rate over the last years.”

Extra public spending could be paid for by a windfall tax on energy companies, he said.

Although Charles Clarke, a long-time critic, and John Prescott clashed over the leadership issue there was little open dissent. Mr Clarke — who has previously called on Mr Brown to stand aside for a new leader if he cannot turn Labour’s fortunes around — said that he was “very sceptical” that he was capable of transforming his performance and told The Politics Show on BBC One: “Therefore I think he probably should stand down.”

MPs thought they could not afford delays in resolving the leadership issue, he said. “The one thing which I think is completely unacceptable is to ignore the real political situation in the country and drift along, assuming we will somehow pull it around . . . It won’t be all right on the night.”

Barry Gardiner, who lost his job as Mr Brown’s forestry envoy when he joined calls for a leadership contest, likened the conference to a family “putting on a good face” at Christmas.

John Prescott, the former Deputy Prime Minister, dismissed the rebels such as Mr Clarke as “bitter”.

But one senior government figure said: “The danger is that we stay loyal and just kill ourselves. I’m not vindictive. I want Gordon to succeed but I don’t think he has it in him.

“There are two schools of thought running at the moment; one is that David Miliband has got it sewn up, and is getting on with introducing himself as widely as possible at this conference,” a source said.

“But there is also a ‘no change, no chance’ camp who believe there need not be a candidate at the point Brown is ousted.”

Mr Brown’s rating in the polls could suffer a further setback with the prospect of an increase in taxes as result of the credit crunch.

Leading economists have predicted that government borrowing will have to rise as the Treasury’s income is cut following the slump in City earnings.

Some forecasters have predicted that public borrowing could reach £100 billion a year, giving Britain a huge budget deficit.

Times Recommends

• How I lost the gift of joy for a while
• Why Ann Widdecombe has got it wrong
• Alas, it’s the end of the road for petrolheads