The latest lobbying allegations to hit Parliament are "a new low for British politics", a senior MP has said.
Shadow defence secretary Jim Murphy said voters would rightly be "sickened" at reports that peers were prepared to lobby in return for cash.
And campaigners said the government had just weeks to introduce new rules or risk presenting a "green light" to lobbyists to carry on as they were.
A third peer, Lord Laird, has resigned from the Ulster Unionist Party after being caught up in the same sting, which followed the resignation from the Conservative Party last week of MP Patrick Mercer.
All deny any wrong-doing but have referred themselves to Parliament's sleaze watchdog.
Mackenzie told Channel 4 News: "I accept that clearly the rules were got around" when Lords asked other peers to arrange functions on their behalf.
Jim Murphy said voters would be 'sickened'
Commons and Lords codes of conduct prohibit "paid advocacy" by parliamentarians.
Cabinet Office minister Francis Maude expressed confidence that lobbying reform would proceed before the election as Labour demanded urgent cross-party talks on the stalled introduction of a register.
David Cameron warned in 2010 that lobbying was the "next big scandal waiting to happen" and changes were promised in the coalition agreement.
But there has been no sign of legislation, with Deputy Prime Minister Nick Clegg blaming his Tory coalition partners for the delay.
"We are going to do this. We need finally to resolve the issues about scope and so long and then we'll get on with it," he told the BBC's Sunday Politics, adding that he would be "astonished" if both that and recall powers were not in place by 2015.
Murphy told the Sunday Politics: "The public, who have looked on with a sense of astonishment and with a sense that there is one rule for those who govern and another set of rules for those who are governed, will just be utterly sickened by it, and they are right to be sickened."
A recall power was needed for MPs guilty of "serious financial misbehaviour that brings politics, parliament and the process into disrepute", he said.
And parties had "only scratched the surface" of what needed to be done to clean up the Lords, including expelling those who broke the law.
"I think the public probably thought things couldn't get any worse. This is a new low for British politics."
A spokesman for the Unlock Democracy campaign group told The Huffington Post UK: "I wouldn't say it's a new low, because it's kind of more of the old low.
"As David Cameron said, this is a scandal waiting to happen - unfortunately he said that in 2010, and he has been proved right several times."
There was no mention of a lobbyists' register in the recent Queen's speech, he said, and urged ministers to act soon if new rules - including a recall power for MPs - would be in place before the next General Election.
"If not, it will be taken as a green light for the lobbying industry to carry on with business as usual," he added.