They’re all the same, they’re all on the take. This is the complaint that rings out from a thousand radio phone-ins to a million kitchen tables. Yesterday David Cameron took the first, confident step towards tackling this public anger against MPs.

Ever since the storm about the uses and abuses of allowances erupted, the battered Palace of Westminster has been drifting. The Speaker should have been at the helm, showing that MPs collectively understand the voters’ rage. He should have showed that he understood that his responsibility was, first and foremost, to the integrity of Parliament.

Instead, Michael Martin has behaved like the shop steward he once was, keener to protect the perks of MPs than reform the discredited system that he has presided over. He has been scornful of those colleagues who have urged change and dismissive of the public. It is not the convention for MPs to call for the Speaker to go, but go he must.

Gordon Brown had a chance to salvage the reputation of the Commons. He blew it. With one bizarre YouTube performance he sabotaged himself. He should clean house (or get his brother to do it). Instead, as is typical of him when disaster strikes, Mr Brown, apart from a clumsy apology, has retreated into his “business as usual” default mode, letting the furore crash on around him.

Mr Cameron filled that leadership vacuum yesterday with a self-assured, articulate announcement. He cannot make his party above criticism. It is too late for that. But at least he showed that he fully comprehends the public’s attitude. There are arguments that can be made in defence of MPs’ claims. But Mr Cameron was right not to repeat them. He was right to give an unambiguous apology for the actions of some of his fellow Tories. And he was right to go beyond lawyerly cavils and say of some of the claims: “I don’t care if they were within the rules, they were wrong.”

And with his words, came action. He has led by example: he will repay the only maintenance payment he has received and has ordered his Shadow Cabinet colleagues to return excessive expense claims.

His plans for cleaning up the act of his MPs are a good start. It was secrecy that allowed the excesses to flourish, so it is right that Tory MPs should be upfront, publishing their expense claims on the internet as they make them. Banning his MPs from indulging in the dubious practice of “flipping” their homes will do something to restore the credibility of politicians; likewise, Mr Cameron’s promise that Tory MPs will have to pay capital gains tax on the sale of any property for which mortgage interest payments have been paid by taxpayers. In this property-owning democracy, it is vital that the public do not feel that there is a political class that lives by different, less strenuous rules.

Perhaps the most impressive element of yesterday’s announcement is that Mr Cameron has taken a gamble. It is a risk to threaten to withdraw the whip from those who refuse to abide by his rules. It is said that Mr Cameron needs a Clause Four moment. MPs’ expenses are not an ideological shibboleth, but his leadership on this issue shows that he is willing to dictate terms to his party. The swimming-pool-owning tendency on the Tory benches is a force to be reckoned with, and he may have to take the political hit of expelling senior MPs.

Mr Cameron said that what he has done is just a start. It may be a long time before the words “Honourable” and “Member” are met with more than a sneer or a snort; and much longer before the public will agree to proper terms for its Parliamentarians. But in this debate on MPs pay, at least the Conservative leader has done what he is paid for. The Leader has led.