Cabinet minister Baroness Warsi was facing an investigation into her parliamentary expenses today 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.

Liberal Democrat backbencher Bob Russell suggested that the matter should be investigated by the police. "I think there's a prima facie case for this to be looked at by the police," he said.

In a further embarrassment for Lady Warsi, the most senior Muslim politician in Britain, she was forced to admit failing to declare rental income on a London flat in the Lords register of interests.

She said the omission was due to an "oversight", adding that she had reported the letting of her Wembley flat in the Register of Ministers' Interests.

The arrangement had also been declared to the Cabinet Office and HM Revenue and Customs, she said.

The peer bought the property in 2007 but moved closer to Parliament when she became a minister in 2010, after which she began letting the Wembley flat.

Peers are required to declare sources of income of more than £500, although the annual rent on a London flat is likely to be many times greater than that.

In a statement last night, Lady Warsi said she contracted to buy the flat in September 2007, but it was not due to be ready until the following year.

In the interim she stayed predominantly at two hotels but also, for "occasional nights", at an Acton property occupied by Mr Khan.

"The completion date for the property was slightly delayed, and not having made advanced bookings for these hotels, there was a period of around six weeks when I spent occasional nights at a flat in Acton, which was occupied by Naweed Khan, at the time a member of Conservative Campaign HQ staff," she said.

"For the nights that I stayed as a guest of Naweed Khan, I made an appropriate financial payment equivalent to what I was paying at the time in hotel costs.

"In March 2008, I moved into the flat in Wembley. As I was living in the property, it was therefore not registrable on the Register of Lords' Interests.

"Mr Khan said he stayed at the house belonging to Dr Moustafa between July 2007 and November 2008 while working in central London.

"In the early part of 2008, for a short period, Baroness Warsi stayed with me," he said in the statement.

"I confirm she made a financial payment on each occasion, which compensated for the inconvenience caused and additional costs incurred by me as a result of her being there."

Conservative deputy chairman Michael Fallon said: "These sorts of thing are always embarrassing but the key thing here is that Lady Warsi has admitted she's made a mistake, she's apologised for it.

"She's corrected the record now and she's very happy to cooperate with any investigation back into her claims and I think it should be left at that until any investigation is reported."