Gordon Brown yesterday endorsed radical measures to put a revived parliament back at the centre of British political life, in a reform package designed to revive his flagging constitutional agenda and restore MPs' lost credibility.

The prime minister set out ideas to curb the power of whips and surrender to MPs important controls over the way Westminster business is conducted. In future, MPs would elect all select committees, take control of the Commons' business programme, and be given a greater chance to introduce legislation.

Brown has asked one of parliament's biggest advocates of reform, the Labour MP Tony Wright, to chair a quick all-party inquiry into parliament. It will examine:

• How parliament can be strengthened in its scrutiny of the government.

• How Westminster connects with the public.

• How control of parliament's daily business can be wrestled away from the government and its whips.

Wright, chair of the all-party public administration select committee, made the suggestion of a "new special committee of authoritative reform-minded MPs" in a private letter to Brown on 1 June, saying his ideas would not threaten the government's legislative programme, but "would help make a more vital Commons from which other reforms would flow".

A number of the measures under consideration have been championed in the Guardian's A New Politics debate.

Wright argues, in common with other MPs, that the expenses scandal and lack of respect for parliament stemmed partly from the fact that the role of MPs trying to hold the government to account had been reduced to one of "heckling a steamroller".

The announcement on reform came on the day Brown received some good news as the first increase in industrial output in more than a year signalled the economy was recovering from the sharpest slump since the second world war.

Wright told the Guardian he did not know how long his committee would take to complete its work, but its proposals are likely to dovetail with the election of a more reform-minded Speaker, such as the Conservative MP John Bercow. The former foreign secretary Margaret Beckett announced yesterday that she was joining the crowded field for the Speakership once an election is triggered by the stepping down of Michael Martin, widely blamed by MPs for the expenses scandal.

Conservative MP Ann Widdecombe today also announced her decision to run with her aim being to "clean up the place" and connect with the public.

Government sources said they had partly picked up Wright's proposal after MPs found themselves unable to table a motion of no confidence in the Speaker unless the government tabled the motion. The aim would be to give MPs far more time to force debates and meaningful votes, while ensuring there was enough time for the debate of government bills.

Jack Straw, the justice secretary, wants Wright's committee to look at the possibility of using well-supported public e-­petitions on specific issues as a way of requiring MPs to hold debates on issues that matter to voters. "We need to find a way of ending the distance between MPs and the public, and this may be it," he said. Until now the government has refused to provide funding for the project.

The communities minister, Shahid Malik, was yesterday facing fresh questions over his expenses claims only a day after the new independent system of inquiry into compliance with the ministers' code of conduct had given him a clear bill of health. The inquiry had been conducted by Sir Philip Mawer.

Malik was facing questions over why he was claiming money from the taxpayers' office costs allowance to fund an office in his constituency home in Dewsbury when he was making claims for his office costs elsewhere in his constituency at the same time. Malik was also making a claim for a home in London, to which he was entitled, so long as it was designated as his second home.

Number 10 will be concerned if its new thorough independent review into compliance with the ministerial code failed to pick up any wrongdoing. Downing Street had initially refused to publish its inquiry into the initial allegations against Malik, but changed its mind yesterday.

David Cameron said the prime minister's proposals were a smokescreen to distract attention from Brown's loss of authority, and used prime minister's questions to call for an immediate general election. The Liberal Democrat leader, Nick Clegg, urged Brown to cancel the Commons' 72-day summer break to ensure the reforms are in place by the autumn.

Brown, scrambling to assemble a more radical final year agenda, is in a race against time to revive his becalmed constitutional reform programme. Legislation will be rushed through parliament to end Westminster's system of self-regulation and impose a new code of conduct on MPs in the wake of the expenses scandal.

The prime minister also proposed legislation to introduce a largely elected second chamber, but skirted around plans to make the attorney general independent of the government.

In a sign of the seismic shifts in Labour thinking, Tom Watson, the former Cabinet Office minister and one of Brown's closest allies, writing in the Guardian today, calls for a move towards an alternative vote system to "help rebuild the trust and authority given to our elected representatives".