Leading article: A reshuffle that betrays the Prime Minister's weakness

Until yesterday, the Prime Minister had surely hoped that by reshuffling his Cabinet he would be able to put behind him the losses in Thursday's elections, renew his Government's sense of purpose and stride out with fresh confidence towards the election that really matters. The next Cabinet line-up, announced in dribs and drabs through yesterday, even as the extent of Labour's wipe-out in county council elections was becoming clear, showed how comprehensively he had to jettison that plan.

The new Cabinet has a distinctly old Cabinet feel. The only one of the great offices of state to change hands was the one already vacated by the Home Secretary, Jacqui Smith. That post goes to Alan Johnson. Depending what the former Health Secretary makes of his new berth, it could be seen in retrospect as a poisoned chalice or a springboard to even higher things.

The point is that by the time bright-young-thing James Purnell had published his venomous resignation and John Hutton had announced, in rather more dignified fashion, that he would neither remain at the Ministry of Defence nor contest his seat at the next election, Mr Brown found himself scrambling to fill vacancies rather than shape an election task force. That he did not move – or remove – either the Chancellor or the Foreign Secretary, despite well-sourced reports that this was his intention, only demonstrated how limited was his freedom of manoeuvre. After days of high drama in Westminster, he faced a government with multiple vacancies, but not the right vacancies, and he lacked the authority to mould the new Cabinet to his will.

This is not, to put it mildly, a good position for a Prime Minister to be in. The first real proof that Tony Blair's power was on the wane was when his later Cabinet reshuffles started to go wrong, because people refused to move or declined to serve. But Mr Blair never faced such a train wreck as the one that Mr Brown had to watch in slow motion this week. Caroline Flint's broadside, following her resignation as Europe minister, was a classic of its kind. Ditto the way in which Mr Purnell flounced out at the eleventh hour, demonstrating an unbecoming mixture of overconfidence and inexperience.

In the event, both may have overestimated their capacity to wound. Nor should it be forgotten that Mr Purnell – like many, but not all, those who resigned – had been touched by the expenses scandal. There is nothing like a bit of pseudo-altruistic indignation to deflect incoming criticism.

It is true that some of the public hue and cry over expenses has been exaggerated; there have been times when the pursuit of individual MPs has resembled a witch-hunt. Little distinction has often been made between claims for biscuits, wide-screen televisions and the proceeds from "flipping" residences. But it may also be observed that the distinction in the public mind between the conduct of those who have gone, such as Hazel Blears, and those who remain, such as Alistair Darling, may not be sharp enough to support the Prime Minister's claim to be cleaning up British politics.

The new Cabinet offers a few novelties. Sir Alan Sugar's appointment as Enterprise "tsar", with a peerage but no Cabinet responsibility, is a transparently populist move, but not necessarily the worse for that. Lord Adonis's promotion to Transport Secretary rewards the good job he has done as junior minister, while regrettably increasing the ranks of peers in government. The appointment of Glenys Kinnock, to replace the indignant Ms Flint, at last gives Britain a known Europe-friendly face in Brussels.

The council election results that provided the backdrop to Mr Brown's reshuffle, however, opened the much bigger question of how long this Cabinet – and the Prime Minister – can last. In starting his press conference yesterday with an apology and a blunt acceptance of responsibility for Labour's losses, Mr Brown struck the right tone and made the best of a bad job. In common with many top politicians, he has the knack of rising to adversity. Resilience – a word he deployed several times – is a necessary attribute for leadership.

But this does not alter the fact that Mr Brown has presided over one of Labour's worst electoral performances ever and the party has lost control of the only four English county councils it still had. The results were a triumph for David Cameron and the Conservatives. While no disaster for the Liberal Democrats, they provided scant consolation for Nick Clegg, who has performed commendably in recent months.

What happened on Thursday only underlines how far this government has been discredited. The need for an election is overwhelming. In insisting yesterday that he was committed to cleaning up politics, instituting democratic renewal and bringing about economic recovery, the Prime Minister was saying all the right things. With determination and a little luck on the economy, none of this need be impossible. The doubt relates not to his strength of will, but to whether his authority will last that long.