Cabinet minister Baroness Warsi was facing an investigation into her parliamentary expenses amid allegations she claimed for accommodation while staying at a friend's house rent-free.

The House of Lords Commissioner for Standards, former chief constable Paul Kernaghan, is being asked by Labour MP John Mann to conduct an inquiry into the Tory peer's claims.

Lady Warsi, the co-chairman of the Conservative Party, was advised by former sleaze watchdog Sir Alistair Graham to stand down from her role as a Cabinet Office minister pending the outcome of any inquiry.

Downing Street has made no show of support for the peer. Tory deputy chairman Michael Fallon said only that Lady Warsi "believes" she acted within the rules, but he admitted that the controversy was embarrassing for the party.

Lady Warsi insisted she made an "appropriate payment" to her friend - Tory official Naweed Khan, who is now one of her aides - for the nights she stayed at the property in Acton, west London. Mr Khan supported her assertion, releasing a statement saying she made a payment each time she stayed.

But the property's owner, GP and former Conservative donor Wafik Moustafa, denied receiving any income from either Lady Warsi or Mr Khan.

The peer, now a Cabinet Office minister, was claiming Lords subsistence of £165.50 a night at the time the allegations relate to, in 2008.

Sir Alistair, a former chairman of the Committee on Standards in Public Life, said: "At the moment it all looks very muddy and blurred and worthy of a full investigation."

He suggested that if there was an investigation Lady Warsi should relinquish her ministerial office until any inquiries were complete. "I personally am always of the view, when ministers face very serious allegations that seem to have some strength to them, then it's better that they stand down from their ministerial post while that investigation takes place, but of course that is a matter for the Prime Minister," he said.

Mr Mann said he would be writing to the Lords standards commissioner requesting an investigation. "If you are paying no rent where you are staying, you can't possibly be claiming subsistence for staying there," he said.