Evan Harris, a Liberal Democrat MP who had tried to force through extra measures during this week's debate, said members from all sides would continue to press for change.
Gays could still be prosecuted for group sex while heterosexuals could not, he said. He has also called for adults prosecuted in the past for gay sex with 16- or 17-year-olds to be removed from the sex offenders' register.
The group will campaign, too, for equal pension rights and other forms of recognition for gay couples.
Dr Harris (Oxford West and Abingdon) said his attempts on Monday had been useful. "I will continue to press for an end to discrimination in sexual offences, which waste a lot of court time and in which the state has no interest," Dr Harris said.
Alun Michael, the Home Office minister, said in Monday's debate that he was sympathetic to calls for a change in the law on group sex. A case is currently being taken to Europe for a man who videoed two others having sex, but the Government is opposing it.
The leading Labour member on the new group is expected to be Kalli Mountford (Colne Valley) and there will also be a Conservative sponsor, though none has yet been chosen.
The gay rights organisation Stonewall also vowed to continue campaigning for full equality for gay people. It wants to overturn the ban on gays in the military, and the legislation which prevents advice being given to gay teenagers by local authorities and state schools.
"It is by no means the end of the battle to secure full equality for lesbians and gay men but it does mark a turning point. MPs have made it clear they believe the law can no longer discriminate in the way it has for generations," said Angela Mason, Stonewall's executive director. Peter Tatchell of the gay rights group Outrage said he would be pushing for legal recognition of same-sex relationships and equal parenting rights for gays and lesbians.Reuse content