An extraordinary race to clear up the mess of MPs’ expenses began yesterday with David Cameron, the Commons standards committee and Gordon Brown challenging the sedate pace of reform envisaged by the Commons Speaker.

The Tory leader led the way yesterday morning, ordering his frontbench team to publish by July 1 full details of how they spend their expenses and to name by April 1 any family members who work for them. They will have to do so in order to remain on the front bench and, although he has no power to force his backbenchers to do the same, Mr Cameron made plain that he expects them to follow suit.

The urgency was a vivid contrast to the review of perks and expenses announced by Michael Martin, the Speaker, the night before, which suggested a conclusion in the autumn. There was ridicule at Westminster that he had picked a team of Establishment figures to carry out the review. Some had been mired in controversy in the past.

Privately, MPs expressed dismay and accused Mr Martin of ensuring that some of the most reactionary MPs in Parliament would be able to dictate the pace and scope of any changes. Among those leading the work is David Maclean, 54, a former Conservative Chief Whip, who sought to exempt MPs from freedom of information laws by bringing forward backbench legislation last year. It was blocked eventually in the Lords. He also admitted using Commons allowances to buy a quad bike for £3,300 for use on his large rural constituency in Cumbria and has been a vocal critic of moves to modernise the Commons.

Another is the Labour MP Sir Stuart Bell, 69, a former colliery clerk from the party’s traditional right wing regarded by many colleagues as an arch conservative. He was knighted in 2004 for services to Parliament. Mr Maclean and Sir Stuart have been MPs for 25 years and are seen as Commons insiders.

The third is Nick Harvey, a Liberal Democrat MP, who is the official spokesman of the House of Commons Commission, its governing body, and therefore the voice of the parliamentary Establishment. One of his roles is to defend the commission during monthly questions from MPs in the Commons.

In another sign of incremental rather than radical change, the Speaker told MPs that options for reform should be built “on the existing regime governing allowances”. All three MPs who will head the review sit on a body called the Members Estimates Committee, which is responsible for overall spending on MPs’ expenses, periodically reviews the rules for MPs allowances and considers disputes over individual claims. But its six MPs all double up as members of the House of Commons Commission.

Although the three backbenchers, drawn from each of the main parties, have been asked to “take the work forward” they will do so on behalf of the estimates committee chaired by the Speaker.

Mr Martin has himself been a controversial figure since his election as Speaker in 2000. He has been the subject of repeated publicity over his expenses claims, including almost £50,000 in air travel and £4,000 in taxi bills run up by his wife Mary, past salary payments to her for constituency work and his claims for housing costs, despite having state apartments at the Commons. Mr Martin has also blocked fuller disclosure of MPs’ expenses claims.

There are two frontbench representatives on the committee. One is Harriet Harman, the Leader of the Commons, who is under investigation by the Electoral Commission over a donation of £5,000 to her campaign to become Labour’s deputy leader. The other is Theresa May, Ms Harman’s Tory Shadow, who regards herself as a moderniser but has been sidelined under David Cameron. One MP told The Times: “These are not the people who should be looking at MPs expenses. It should be given to somebody completely outside Parliament.”

The Standards and Privileges Committee, chaired by Sir George Young, whose report last week led to the downfall of Derek Conway, exploited the mood of dissatisfaction swiftly by issuing a surprise statement saying that all MPs, not just frontbenchers, should be required to register by April 1. That is likely to be voted on by the Commons, preempting at least some of the work foreseen for the Speaker’s committee.

Mr Brown finally released a letter to the Speaker last night, which had been trailed all day. in which he said that he was requiring all Labour MPs, backbenchers as well as frontbenchers, to be fully transparent in their declarations. In a clear move to try to outflank Mr Cameron, he said that they must abide, not by April but as soon as possible, with the Committee on Standards and Privileges’ opinion that the employment of family members should be declared.

He embraced Mr Martin’s review but made plain to the Speaker he expected robust conclusions. He wrote: “I believe your review will need to be a deliberative and orderly process, which delivers genuine and lasting reform. I, like all Members, would not favour a quick fix, which would fail to solve the problem in the long term.”

Tony Wright, chairman of the Public Administration Committee, said that Parliament must not be allowed to review the matter of expenses and allowances itself. He said that while politicians faced a “scandal a day”, the Derek Conway affair was of a different order: “That is corruption, and should be dealt with as such.”

Calling the issue of MPs allowances a “scandal waiting to happen”, he added: “Club government has to end. Parliamentary privilege is about protecting unfettered speech, not defending the indefensible.”

He called for MPs to put themselves under a new anticorruption law and said that the Committee on Standards in Public Life, which operates outside Parliament, must begin an immediate inquiry into expenses. He called the issue the first real test for the new chairman, Sir Christopher Kelly, who replaced Sir Alistair Graham last year. Dr Wright claims that Sir Alistair had wanted to conducted an inquiry into expenses but was warned off.

“I take the view that our political system is pretty clean, but it is no good just saying this unless we attend to those areas that do need attention. This is one of them. Unless people can have confidence in the integrity of their Parliament, MPs can blather all they like but nobody will take much notice of what they say or do. Then we really shall be in trouble.”

A number of MPs have expressed concern to The Times about the way the “fees office”, which administers expenses, currently operates. They said that different people offer conflicting advice and that very few requests are dealt with formally. Most discussions about expenses take place orally with no written record.

This comes the day after The Times disclosed that the Clerk, the Commons chief executive, had seen his grace-and-favour home given a £100,000 overhaul without the authorisation of MPs.

Martyn Jones, a Welsh Labour MP, said: “I know colleagues have asked for advice and it has turned out to be wrong. I don’t blame them: the rules are so convoluted it tends to show what we have inflicted on ourselves, but if you really want to fiddle you can still fiddle and this vast bureaucracy is not doing anything to prevent it.”

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