The House of Lords must be scrapped and replaced with an elected chamber after allegations peers offered to change the law for payment, according to a West Midlands MP.

Lorely Burt (Lib Dem Solihull) backed proposals peers found to have behaved improperly should be thrown out.

The MP backed a Commons motion calling for “urgent action to restore trust in Parliament as an institution and in politics as a profession”.

Members of the House of Lords caught in the controversy include Lord Snape, the former MP for West Bromwich East, accused by a newspaper of offering to amend legislation for payment.

He denied the claims, and asked for an opportunity to clear his name in an ongoing House of Lords inquiry.

Lord Snape was one of eight members of the Lords referred to by Liberal Democrat spokesman David Heath this week, when Mr Heath told the Commons: “At least eight are reported to have been prepared to change the law allegedly for cash in their hands. That to me and to many peers is an outrageous position.”

The peer spoke to undercover journalists posing as representatives of a retail chain about proposed laws giving councils the power to levy new taxes on businesses, and agreed to look into their concerns. He discussed acting as a consultant for the business, although did not agree to do so.

Ms Burt said the Lords should have the power to expel members who behaved improperly, but warned there was also “an urgent need to bring forward plans for an elected House”.

She said: “Of course Peers accused of wrongdoing must be given the opportunity to defend themselves, but this latest episode serves to underline the lack of effective sanctions and undermines public respect and credibility in both houses. When people see one set of rules for parliamentarians and another for themselves, it is not surprising they lack trust. Without proper regulation and effective sanctions, politicians and parliament will continue to be held in low esteem.”

Jack Straw, the justice secretary, revealed plans to change the rules so Peers guilty of a criminal offence will be removed, as already happens in the House of Commons.

It could mean Peers with convictions, such as author Lord Archer of Weston-super-Mare and newspaper mogul Lord Black of Crossharbour, would be expelled.

Ministers are considering tough restrictions banning MPs earning extra cash beyond salaries for sitting in the Commons and ministerial duties.

Two of the peers named in the newspaper report, Lord Taylor and Lord Truscott, are expected to be expelled from the Labour Party.

But Labour is expected to wait for the conclusion of the Parliamentary inquiry before deciding whether to withdraw the whip from Lord Snape and Lord Moonie, the fourth peer named.

Liberal Democrat home affairs spokesman Chris Huhne has written to the Metropolitan Police asking them to investigate allegations against four more peers – Lord Berkeley, Lord O’Neill, Baroness Valentine and Baroness Coussins.

Newspaper reports claimed they tabled amendments favouring groups that were paying them. All deny wrongdoing and say they declared their interests.