In a statement to the House of Lords earlier, Lady Royall called the claims "deeply shocking". She pointed out that they were only allegations at this stage but said the claims had been "damaging not just to this House but to Parliament and politics".
She said the matter had been referred to the Lords Interests sub committee, which had already met and investigations were underway.
And she said she believed "tougher sanctions" were needed to deal with peers who broke the rules - currently they cannot be suspended or expelled - and she had written to the chairman of the committee of privileges to ask him to review the matter.
'No grey areas'
The Conservative leader in the Lords, Lord Strathclyde, said the allegations represented a "shocking and depressing moment" for the House of Lords.
"This House has been mired in a grim torrent of criticism about a culture of sleaze," he told peers.
"If these allegations are true those involved have shamed this House," he said, adding there were no "grey areas in the paid advocacy rules".
It's important that we don't pre-judge these investigations but these are serious allegations
But as peers debated the claims, Lord Snape stood up to tell peers: "As one of the people involved in this incident may I first of all apologise for bringing this House, if I have done so, into disrepute.
"But may I say that these are allegations in a Sunday newspaper and may I appeal to noble lords in all parts of the House to allow me the opportunity to refute these allegations before your lordships house and elsewhere."
Lord Taylor told peers: "If I have done anything that has brought this House into disrepute I most humbly apologise."
But he said he wanted to give evidence to the inquiry adding: "I feel within my own conscience I followed the rules and the directions that have been given in this House over the 31 years I have been a member."
Lady Royall "noted" their comments and said the Parliamentary inquiry would undertake its inquiry "swiftly and justly".
The four peers named in the Sunday Times story are former energy minister Lord Truscott, former defence minister Lord Moonie, Lord Taylor of Blackburn and former Labour whip Lord Snape - all of whom deny any wrongdoing.
Lord Truscott did admit to having had "discussions" with a reporter, but said that "to suggest I would offer to put down amendments for money is a lie".
Lord Moonie acknowledged discussing a fee of £30,000 but said he had not done anything "outside the rules".
Taking part in a question-and-answer session at the Foreign Press Association in London earlier, Prime Minister Gordon Brown said: "It's important that we don't pre-judge these investigations but these are serious allegations and we are determined to get to the bottom of these allegations, and whatever action needs to be taken will be taken."
Meanwhile the Lib Dems say they have written to acting Metropolitan Police commissioner Sir Paul Stephenson asking for an investigation to take place.
Home affairs spokesman Chris Huhne told the BBC: "We need to get to the bottom of this and make sure the public realise that this is not just a bunch of politicians being judge and jury in their own courts."
SNP MP Angus MacNeil, whose complaint sparked the "cash-for-honours" probe during Tony Blair's premiership, called for the four peers to be suspended, while an investigation is carried out.
He said: "The House of Lords is unelected, unaccountable and now, with these revelations, it looks completely unsustainable."
If the peers were found guilty of having broken the rules, they could be required to apologise on the floor of the Lords, but cannot be expelled from Parliament or stripped of their titles.
The Sunday Times said its reporters had posed as lobbyists acting for a foreign client, who was setting up a chain of shops in the UK and wanted an exemption from the Business Rates Supplements Bill.
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