Public attitudes to childbirth are to be tested tomorrow in a consultation launched by the Human Fertilisation and Embryology Authority, which will ask whether it is acceptable for a baby to be born, through egg donation, to a woman who is also its grandmother.

The authority is calling for the widest possible participation in the public consultation on the use of donor eggs and sperm to enable infertile couples to have a baby. Views will be sought on whether donors, who are in short supply, should receive more money than they currently receive in compensation for loss of earnings and expenses. But the HFEA also wants to know whether rules should be brought in to prevent close relatives – who would be forbidden by law from marrying – from donating eggs or sperm to each other. It is not uncommon for a sister to donate an egg to her sister - the child is then the genetic daughter and niece of the donor.

But, the consultation will ask, should - as happened recently - a woman be allowed to donate eggs to ensure her infertile daughter can have a baby, when the ensuing child would be both her daughter and her granddaughter?

Prof Lisa Jardine, chair of the HFEA, said that the increasing use of fertility treatment and the increasing openness about the children it produces meant that the whole of society ought to be involved in deciding what was acceptable. "I'm a good example of a generation whose children played with other children in the full understanding that all of those children were of heterosexual couples and had been produced … by a conventional method of reproduction.

"Many of them had not been. We didn't know and the community didn't know."

She cited a New York Times Review cover, which featured two babies described as "twiblings" - they had one father but separate surrogate mothers and were born within days of each other. "The point I really want to make is that this of importance to all of us. These are new kinds of families. They are populating our communities. Genetically, the consequences for the community are bound to become more complicated."

Those parents who now have small children may one day have to explain to them what one of their friends means when he says he is donor-conceived, she said.

"Donation is part of all our lives. Everybody needs to have a view. It is about all of us. It's about new, emerging types of families and how they will impact on all families," she said.

Only about 12% of fertility treatments involve donated eggs or sperm, but the HFEA believes that will rise, or would if there were sufficient donors to fill demand.

The public consultation that begins today asks about reimbursement for donors. At the moment, HFEA rules allow compensation for expenses and loss of earnings up to £250, but not for inconvenience as some other European countries do. In Spain, egg donors receive around £765 and sperm donors £40 per sample. While the HFEA does not want to provide a financial incentive, because donation must be based on altruism, clinics say some donors are left out of pocket. The authority wants to know whether a lump sum should be paid, if the system should be less complicated, and what compensation should be offered.

However the campaign group No2Eggsploitation said any plan to allow financial compensation for egg donors would "lead to the exploitation of young women in financial stress". Another question is over the number of families a single sperm donor is allowed to create. At the moment, the limit is ten, but because of delays in establishing whether the woman becomes pregnant and gives birth to a healthy baby, in practice sperm donors often help no more than two or three families.

Inter-family donation is popular because it maintains genetic links, but the consultation asks for opinions on the social and ethical outcomes. Options that will be canvassed are a ban on the mixing of sperm and eggs between close relatives (those who would otherwise be banned from having sex with each other) or a ban only on the mixing of sperm and eggs between genetic relatives.

The consultation site, which will be open for three months, can be found at www.hfea.gov.uk/donationreview.