Urging fellow peers to suspend Lord Truscott and Lord Taylor, Lord Brabazon of Tara, chairman of the Privileges Committee, said an internal investigation had shown that they had "failed to act on their personal honour".
"This episode has done serious damage to the reputation of the House," he said.
The House had the "inherent" power to discipline its members and must show that it was prepared to take action, he added: "We have to get our house in order."
The Sunday Times also made allegations against two other Labour peers, Lord Snape and Lord Moonie.
The two were ultimately cleared of wrongdoing by the privileges committee but invited to apologise for "inappropriate attitudes" to their duties brought to light during the investigation - which Lord Snape subsequently did.
For the Conservatives, Lord Strathclyde said the actions of all four men "fell short" of the high standards expected of their representatives by Parliament and the public.
But in the case of Lord Truscott and Lord Taylor, he said the Lords must act in a "firm and unified" way to show its "abhorrence" at the way they had broken parliamentary rules.
Lord McNally, Lib Dem leader in the Lords, said he believed the Sunday Times had been guilty of "entrapment" and the rules governing lobbying practices needed tightening.
However, at a time when the reputation of Parliament was being assailed, he said the Lords must show "loud and clear" that it would not condone wrongdoing.
But Labour peer Baroness Mallalieu urged the House to consider less punitive measures than suspension to "make its displeasure known" such as permitting the men to continue sitting but not to speak in debates.
Posing as lobbyists
The Sunday Times alleged the two peers were prepared to change proposed legislation in return for money - breaching parliamentary rules which state that peers should not seek to influence legislation in return for financial inducement.
The reporters were posing as lobbyists for a foreign retail firm which, they claimed, wanted to set up stores in the UK and get an exemption from business rates.
The peers discussed what help they might give them and how parliamentary procedure worked.
Neither men actually accepted any money but the Lords committee found they had broken rules governing the behaviour of its members in relation to paid advocacy.
The allegations against the four men were initially investigated by the Lords sub-committee on members' interests.
It concluded that Lord Truscott had broken rules on exercising parliamentary influence in return for money by agreeing to "smooth the way" for lobbyists, make introductions to other peers and ministers and to lobby officials.
The committee found "clear and plentiful" evidence that he "was advertising his power and willingness to influence Parliament in return for a substantial financial inducement".
Lord Truscott said he followed the rules as they were at the time and had been the victim of "Soviet-style" summary justice.
Lord Taylor's explanation that he was aware the lobbyists were in fact journalists and he had continued to meet them in order to discover the truth was dismissed as "inherently implausible".
Lord Taylor has been suspended from the Labour Party pending a "full disciplinary investigation".
The "cash for amendments" row is one of a series of recent scandals to have damaged the integrity of Parliament.
The police decided not to mount a criminal investigation into the case earlier this year, citing the difficulty of obtaining evidence.
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