David Cameron's swift response yesterday to the damning revelations of abuses of the expenses system by a number of his MPs was a demonstration of the Tory leader's political surefootedness. By announcing that members of the Shadow Cabinet will pay back claims which look excessive (and that if Tory backbenchers fail to do the same they will be expelled from the party) Mr Cameron showed that his concern is for action, rather than words.

The Conservative leader also spoke passionately of why it is vital for the Tories, as a party that has been so critical of Labour's wasteful public spending, to set a moral lead on this matter. Mr Cameron knows that, for the country at large, the abuse of expenses is not only about the sums involved, but feeds into broader concerns over the trustworthiness of the entire political class.

But impressive though Mr Cameron's performance was, shoring up public confidence in the probity of the Conservative Party will be a tough and incremental job. None of the mainstream parties has emerged well from the expenses scandal. But the revelations pose a special problem for the Conservatives because of the party's recent image problems. The news that Tory MPs have claimed taxpayers' money to pay for the upkeep of moats, tennis courts and chandeliers is a serious public relations upset for Mr Cameron, threatening to undermine all his work in brand decontamination.

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Such details serve to reinforce an old stereotype of the plutocratic Conservative grandee, hopelessly out of touch with the majority of British people, while in possession of a grotesque sense of self-entitlement. They could also undermine the central Conservative argument that, if elected, the party will restore rectitude to the public finances. What chance of that, people might ask, when some Tory MPs regard £1,000 gardening bills for their private estates as an appropriate use of taxpayers' cash?

Of course, for the public to blame Mr Cameron personally for the hypocrisy and greed of some of his backbench MPs would be grossly unfair. Mr Cameron did not choose the Conservative parliamentary party; he inherited it when he won the leadership. And those MPs who have abused the system most egregiously are not part – and were never likely to be part – of his frontbench team. Additionally, Mr Cameron has made commendable efforts to modernise the Conservative Party in recent years, ditching the old vote-losing Tory obsessions over Europe, tax cuts and immigration. And his frontbench's focus on improving Britain's public services, rather than devising ways for the wealthy to bypass them, is welcome too.

In recent years, Mr Cameron has dragged his party back from the unelectable fringes to the centre ground of politics. It would be a travesty if the "lord of the manor" lifestyle of some of his more irrelevant backbench MPs were to distract public attention from that achievement.

The Conservative leader made a fine start yesterday in repairing the damage, underlining his political astuteness. But sceptics will inevitably wonder whether he would have announced quite such resolute reforms of the system if these damning details had not come to light in the way they did. Mr Cameron would probably accept that, for all the progress made in recent years, the job of decontaminating the Conservative brand is still not quite complete.