Cabinet reshuffles rarely change the face of politics. On the odd occasions when they do, it is because the Prime Minister has used them to settle a deep-rooted political disagreement with one of the big beasts. The removal of Robin Cook from the Foreign Office is perhaps the most recent example – and that was 11 years ago. A reshuffle like yesterday's, in which the Chancellor, Foreign Secretary, Home Secretary, Education Secretary, Defence Secretary, Business Secretary and Deputy Prime Minister all stayed put, is hardly the stuff of history.

The one major policy issue thrown open by this round of ministerial musical chairs is the future of Heathrow. The outgoing Transport Secretary, Justine Greening, was a prominent casualty, shoved into a less important job because she stuck stubbornly to present government policy. The Aviation minister, Theresa Villiers, was also shifted, though she looked pleased enough because she moved up into a vacant cabinet job. But as the Mayor of London, Boris Johnson, was quick to observe, the only point in removing both ministers must have been to reopen the question of whether Heathrow needs that third runway which Greening so adamantly opposed.

It remains to be seen whether other policies are to be altered or abandoned by the newly reshuffled ministers. Andrew Lansley did not want to be moved out of the Health Department, after years devoted to studying the way the NHS is managed. His place has now been taken by Jeremy Hunt, who knows more about public relations than he does about running hospitals. His appointment may herald a softening of policy, or perhaps Mr Cameron just thinks he can do a better job than Mr Lansley at selling it to the voters.

It is not obvious either what demoting Kenneth Clarke from Justice Secretary to an ill-defined economic role in the Cabinet means. The day brought mixed news for George Osborne. His allies did well out of appointments in the junior ranks, but at cabinet level he failed to get someone with a more managerial mindset than Iain Duncan Smith installed in charge of the high-spending Work and Pensions Department. And he has an ex-Chancellor looking over his shoulder. But that does not necessarily imply a change in policy.

However, while the reshuffle reveals few specifics about government plans, it is an indication of which way David Cameron is leaning. There were two Tory ministers in the old cabinet line-up who were particular targets of hostility from the right wing of the Conservative Party. One, Baroness Warsi, has been removed from the Cabinet and shifted into a tokenistic-sounding job at the Foreign Office. The other, Mr Clarke, no longer has a department to run, his place taken by the rapidly promoted Chris Grayling, a believer in keeping criminals in prison, who once had to apologise for remarking that owners of bed and breakfast hotels should have the right to discriminate against gay couples.

Other good news for the Tory right was that Owen Paterson has been brought back from Northern Ireland to run the Environment Department, though he is no friend of environmentalists.

David Cameron faced a difficult choice yesterday, with his Government trailing in opinion polls, strains appearing in the forced marriage with the Liberal Democrats and the Conservative Party fractious and divided. As he planned his reshuffle, he could have kept public opinion at the front of his mind, or the alliance with the Liberal Democrats, but he chose to ignore both to placate his right wing. This was an exercise in party management that will do little for Mr Cameron's standing in the country.