A Labour peer has denied any wrongdoing over allegations she wrongly claimed approximately £80,000 in allowances.
Baroness Uddin, who is being investigated by the House of Lords, told the Today Programme she thought the rules needed to be overhauled so peers' integrity and intentions were not questioned.
Baroness Uddin did not want to go into her "particular circumstances"
She said: "I think we just simply bring the rules up to date."
Angus Robertson, the Scottish National Party MP for Moray, has referred complaints about Baroness Uddin and Lord Clarke to the Clerk of the Parliaments, Michael Pownall.
Mr Robertson has also referred complaints about four other peers to Scotland Yard for investigation.
Peers who are not in receipt of a ministerial salary are entitled to claim for £174 a night to allow them to stay near parliament, as well as daytime subsistence and office expenses.
Baroness Uddin, the first woman Muslim to sit in the Lords, has been accused of declaring a flat in Kent as her main home, allowing her to claim approximately £80,000 in allowances.
Absolute transparency is needed and absolute accountability
This consists of the benefit of £174 a night towards staying in her London house.
In her first broadcast interview since the claims were made, she insisted that the rules governing allowances were too ambiguous.
"I think I'll have to explain at an appropriate time my own particular circumstances but obviously I'd like not to go into [them] otherwise that would be in the public arena," she said.
"Generally I think it's absolutely right that people aren't necessarily saying that they're sure about the rules or anything like that.
"They're saying the rules are too loose and they should be very, very specific so people's intentions and integrity are not questioned."
A Labour peer and former party chairman, Lord Clarke of Hampstead, has referred allegations that he had abused the allowances system to the House authorities.
However he has apologised in the House of Lords.
He said: "I tender my humblest apologies to the house and I've asked the clerk of the parliaments, as accounting officer, to investigate these issues and I will of course co-operate fully with that and any other inquiries."
Another Labour peer, Baroness Thornton, a junior minister in the Whips office at the Lords, has also denied abusing the allowances system.
She has declared a bungalow she shares with her mother in the north Yorkshire town of Shipley as her main home, allowing her to claim overnight allowances for the past eight years on her London home.
Baroness Thornton, who declined interview requests, is not currently under investigation but a complaint about her has been referred to Scotland Yard by the SNP.
In a statement, she said she "deeply resented" reports that she was feathering her own nest.
She said: "I am proud of my city and want to support Bradford as much as possibly, I may have left Bradford for a while but Bradford never left me."
She said her mother became seriously ill in 2002 and since then she has travelled to Yorkshire each weekend.
"My husband is a Huddersfield man, and I have always intended to make our home here in Yorkshire as our children grew up and we were able to do so.
"This would mean commuting to London each week to work - both to run my business and more recently to work in the House of Lords as a government whip.
"This is what I do, week in and week out."
Mr Pownall is expected to make a report on the complaints to the senior Lords on the Lords Privileges Committee
Peers from all three main political parties have faced questions over their allowances.
Baroness de Souza, convenor of the 201 crossbenchers who sit in the House said: "The pervasive understanding is that, because no salary is paid, the allowances can be claimed in full.
"I think there is a problem there because some people interpret it one way and some people interpret it another way.
"What I think has happened - and this is across the House - is that there are a very few cases where people have claimed a London allowance for staying overnight and claimed that their main house is outside London, when that's patently not true."
The prime minister has promised a review of peers' expenses
Christopher Dickson, a senior counsel for the Accountants Disciplinary Scheme and formerly assistant director at the Serious Fraud Office, said that some peers could have a case to answer under the 2007 Fraud Act.
"Any potential offence would be under the Fraud Act and that requires three things to be proved," he told the BBC.
"First, it requires you to prove that a false statement has been made - an untrue statement.
"Secondly, that the person who's made the statement has gained and thirdly that it's been done dishonestly."
Lord McNally, leader of 71 Liberal Democrat peers, called for reform.
"Absolute transparency is needed and absolute accountability - just to deal with what has been a complete collapse in public confidence in parliament," he said.
"By the time parliament returns for the new session in November we should have that system we are proposing in place for a set allowance which is taxable and which accountable and I think that would settle most of the concerns people have about Lords expenses."
In his statement on constitutional reform last week, Gordon Brown made it clear that the House of Lords also needed to change.
He told the Commons that he had written to the Senior Salaries Review Body to ask it to examine the financial support system in the House of Lords.
He said: "For the first time there will also be legislation for new disciplinary sanctions for the misconduct of peers in the House of Lords."
Last month the Lords Privileges Committee voted to suspend two Labour peers, Lord Truscott and Lord Taylor of Blackburn, for six months over the so called "cash for influence affair".
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