Select committee chairmen should be elected, a committee of MPs has recommended.

The special 18-member select committee on reform of the House of Commons was appointed in July and chaired by Labour's Tony Wright, who also leads the Commons public administration committee.

It has called for radical changes to the way the Commons runs its business, with backebnch MPs allowed to set the agenda for one day a week.

At present the government decides business, with allocated days for opposition debate.

The MPs have recommended a new backbench business committee elected by secret ballot of all members, "responsible for all business which is not strictly ministerial".

At least one day a week, or its equivalent, should be given over to "discussing matters that members feel should be prioritised".

The new committee would work with government and opposition to put a weekly agenda to the House for its decision.

"This would enable business in the House to be conducted in new ways.

"The committee also wants the House to decide for itself when it sits and calls for the new Parliament to decide promptly on the issue of September sittings."

Under the committee's proposals the chairs of most select committees would be directly elected by secret ballot of the House using the alternative vote.

"Members of most committees should be elected from within party groups by secret ballot."

The committee recommends a reduction in the numbers of members on each committee and in the number of committees.

On petitions and "representations from the public on issues of concern," the committee recommends the procedure committee should become the procedure and petitions committee for a trial period from January 2010.

"The main focus of the House's agenda for engagement with the public should shift beyond the giving of information to actively assisting the achievement of a greater degree of public participation," the committee said.

"Discussions should begin to find ways to strengthen the petitions system, with the possibility of introducing e-petitions."

Tony Wright, chair of the reform committee, said: "Out of the catastrophe of the expenses scandal, Parliament has an opportunity and obligation to show that it really matters.

"This will not be achieved by one report, but we can at least start a process that I hope the next Parliament will want to carry forward."