Cameron promised to publish legislation by next month to bring in a statutory register of lobbyists. Two Labour peers have been suspended from the party after the claims, while an Ulster Unionist peer has resigned his party whip.
The gay marriage wrecking move was proposed during a passionate Lords debate by Lord Dear, a crossbencher and former chief constable of the West Midlands. He angered peers who support gay marriage by warning that the proposal could provoke a public backlash against gay people.
He said: "I fear the bill, should it become law, could well create such opposition to homosexuals in general that the climate of tolerance and acceptance in this country, that we have all championed and supported and seen flourish over the years, could well be set back by decades."
Insisting the measure would overturn centuries of tradition by altering the concept of marriage, Dear added: "It seeks to divide a nation with an argument that hides behind the concept of equality, when in reality it is about sameness and it stands on its head all considerations of electoral mandate."
But Lord Black of Brentwood, a gay Tory peer and executive director of the Telegraph Media Group, said: "This is 2013. Gay people don't want to be tolerated in this society. They want to be equal in this society."
Black told peers that although he was in what Dear called a "tiny minority", he was "the same as you except that I happen to love a man". He said his decision to enter a civil partnership with his partner, Mark Bolland, in 2006 had strengthened and deepened their relationship in a way he had not thought possible at the time.
Labour's Lord Smith of Finsbury, who was the first MP to come out as gay, said some of the remarks by the bill's opponents were "mistaken, misguided and sometimes rather hurtful".
The Most Rev Justin Welby, the Archbishop of Canterbury, opposed the bill, saying, "The Church has often not served the LGBT communities in the way it should. I must express my sadness and sorrow at that considerable failure."
- Independent