The main party leaders are too eager to close down the MPs’ expenses row. Their unanimity yesterday that the Kelly report should be accepted “in full” is misleading. Their motive, to show that the political class recognises the urgency of putting its house in order, is correct. And so is the implicit warning that MPs should not seek to unravel Kelly.

But the phrase “in full” should not be taken at face value. Kelly, or rather the Committee on Standards in Public Life, is formally just making recommendations to the new Independent Parliamentary Standards Authority, which will produce the rules. Sir Ian Kennedy, the IPSA chairman-designate, has promised a short period of public consultation before the new system starts next spring.

There are also several rough edges to the practical operation of Kelly: for instance about perverse incentives for older MPs to delay retirement and about the proposed rental system. But there is nothing that cannot be sorted by the IPSA, while retaining the thrust of the Kelly package.

Potentially trickier, as the Hansard Society noted, are proposals that require new primary legislation, such as extending the remit of the IPSA to salaries and pensions and giving it powers to investigate and invoke sanctions like the Revenue & Customs, while returning the code of conduct to the Commons. Moreover, putting non-MP members on the Commons Standards and Privileges Committee raises big constitutional issues. Again, these should not delay the bulk of the changes.

But the existing mess also has to be cleared up. The Legg saga on repayments has a long way to go, with some MPs suspected of playing for time over details of their mortgages. This should be clarified quickly, so that voters know who the real rogues are.

As important is showing that Parliament is effective and responding to voters’ concerns. Tony Wright’s committee on Commons reform is due to report soon, but some MPs on it still do not recognise the challenge facing the Commons. So there is a risk that the committee could produce watered-down proposals on public engagement.

Yesterday was a big step, but only a step, towards a system that is publicly acceptable and recognises the real need of MPs to live in two places. But MPs need not only proclaim their conversion to virtue, but also show that the way the Commons operates is changing.