A new report from the Centre for Social Justice has recommended that some rights of same-sex partners who are not biological parents should be downgraded.

The Centre for Social Justice is chaired by Iain Duncan Smith, the former Tory leader.

According to the Family Matters report, lesbians undergoing fertility treatment should not be able to automatically record a civil partner as a second parent.

Instead, it recommends using an adapted “special guardianship” status:

“We believe the desired objectives could be better achieved by giving a same-sex partner special guardianship status rather than by having two females registered as parents, since this is fundamentally incompatible with the heterosexual reality of parentage.

“We recommend that urgent consideration be given to remedy this anomaly, by introducing a status with some of the features of ‘special guardianship’, but which also allows private ordering (rather than a court order) subject to further consideration of the exact circumstances in which this would be appropriate and in accordance with the welfare of the child.”

Last year, Mr Duncan Smith proposed an amendment to retain the requirement for doctors to consider the need for a father when assessing women for fertility treatment.

He said at the time: “Another nail will have been hammered into the coffin of the traditional family and another blow will have been struck against fatherhood,

Stonewall suggested he was equating lesbian relationships with broken homes, adding the implication was “ludicrous”.

The Human Fertilisation and Embryology Act 2008, which came into force in May, means that lesbian couples who are not in a civil partnership can share equal responsibility for a child born as a result of IVF rather than the birth-mother only.

The right is automatic for those in civil partnerships.

However, couples must register their agreement to become joint parents in writing in a prescribed form to ensure they have legal protection if they separate.

The law is set to be expanded in April 2010, when male couples will also be able to apply for a Parental Order to be recognised as the parents of children born through surrogacy.