As he turns his mind from his rain-soaked holiday in Cornwall to his imminent ministerial reshuffle, David Cameron is presented with evidence to support what until now has been confined to mutterings among senior colleagues.
Two of the prime minister's closest allies, George Osborne and William Hague, stand at opposite ends of the cabinet popularity contest, according to this month's Guardian/ICM poll. Nearly half (48%) of voters would like to see the chancellor removed in next month's reshuffle while only 21% are calling for the head of the foreign secretary.
The findings are likely to be seized on by Conservative MPs who believe the government can only revive its chances if it sends out an unmistakable signal that it is rejuvenating its economic policy without embarking on a U-turn over the deficit reduction plan. In the tearooms at Westminster, MPs are saying this can only be done by persuading Osborne and Hague to swap roles.
One senior figure who floated this option thought it was highly unlikely to actually happen: "Will the prime minister sacrifice his chancellor? I doubt it. And I can't see William moving."
The prime minister, a keen student of the Blair years, is instinctively wary of reshuffles. He believes Blair was wrong to think he could refresh his government by reshuffling the pack once a year.
Cameron's view is that Blair ended up with a series of ministers who were in their posts for such a short period they barely had time to understand their ministerial briefs.
He has therefore waited two years to carry out his first substantial reshuffle, keeping to his plan when he became prime minister. But his thesis that reshuffles rarely transform the fortunes of a government is being tested, because he is moving ministers around at the very moment when the government badly needs a fresh makeover as it struggles with the issue that will determine its success – the economy.
Many Tory MPs believe the government is crying out for one bold step: moving Osborne. According to a pamphlet by the centre-right Centre for Policy Studies published this week, the chancellor is unlikely to meet his "fiscal mandate", set out in his emergency budget of June 2010: the elimination of the structural budget deficit, to be assessed on a rolling five-year basis, ensuring that debt as a share of GDP is falling by the final year of his mandate in 2015-16.
But Cameron is resisting pressure to follow the example of Labour's Harold Wilson who swapped the holders of two great offices of state after a failure of economic policy.
Jim Callaghan, chancellor during the 1967 devaluation of sterling, swapped places with Roy Jenkins to become home secretary. Within nine years, Callaghan was prime minister. One Tory MP told the Guardian last week that Cameron would "delay the inevitable" by a year if he resisted this job swap.
Downing Street sources say the reshuffle will involve more than tinkering with the cabinet. It is expected that three cabinet ministers – the Welsh secretary Cheryl Gillan, the leader of the commons Sir George Young and the chief whip Patrick McLoughlin – will return to the backbenches. This will clear the way for younger figures, such as Chris Grayling and Maria Miller, to enter the cabinet.
Some of the remaining ministers are expected to embark on a round of musical chairs. Kenneth Clarke may move from justice to replace Young; Jeremy Hunt may move from the culture department; and Lady Warsi may move on from the co-chairmanship of the Conservative party.
Clarke is facing calls to be removed from his post as justice secretary by 28% of those polled by ICM, a relatively low percentage for such a high-profile figure. This will provide some comfort for Clarke as he fights attempts by No 10 to demote him to replace Young as leader of the House of Commons.
The cabinet veteran, who has been involved in a series of clashes with No 10 over his liberal approach to penal policy, is making it clear in private that he still has much work to do as justice secretary. Messages are also being sent out that the prime minister, who appeared to overlook Clarke's liberal approach when he was appointed justice secretary, will harm his campaign to detoxify the Tory brand if he removes such a mainstream figure.
Only 24% of those polled believe Hunt should lose his job. This figure will no doubt be highlighted by those Tories who believe his critics – who feel he has been too friendly to the Murdoch media empire – inhabit a small world that is of little interest to most voters.
The cabinet ministers associated with some of the government's most controversial policies over the past two years are likely to remain in their posts. Andrew Lansley, who is facing calls from 37% of those polled to be sacked, is expected to remain as health secretary.
Lansley has made clear that he holds the only cabinet post that interests him. It would be difficult for the prime minister to remove Lansley in this reshuffle – he could be vulnerable in a year's time – after he became a folk hero on the Tory benches where many MPs were incensed by the Liberal Democrat campaign against the health and social care bill.
Michael Gove, the education secretary who is facing calls from 36% of those polled to leave, is widely expected to remain. Gove is a close personal ally of the prime minister who believes has been impressed with the speed with which he introduced legislation to create a new generation of free schools.
• ICM Research interviewed a random sample of 1,006 adults aged 18+ by telephone on 24-26 August 2012. Interviews were conducted across the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.
