The fertility regulator, the Human Fertilisation and Embryology Authority, aims to reduce the multiple birth rate.
The bulk of the Human Fertilisation and Embryology Act 2008 will come into force on 1 October.
The findings were published in Human Reproduction, the journal of the European Society of Human Reproduction and Embryology.
Guidance from the Human Fertilisation and Embryology Authority (HFEA) is to be updated in the light of US research.
Dame Suzi, who used to chair the Human Fertilisation and Embryology Authority, claimed the Fairness Commission was not "a gimmick".
In the UK, the Human Fertilisation and Embryology Authority has licensed a number of tightly-controlled research projects into mitochondrial diseases.
She said the Human Fertilisation and Embryology Act "yet again shows itself to be wearing very thin at the seams".
The regulatory body, the Human Fertilisation and Embryology Authority, is due to announce the results of its public consultation next week.
However, any such research, whether on cloned material or not, would require alterations to the 1990 Human Fertilisation and Embryology Act.
Other ways of "getting around" the guidelines, from the Human Fertilisation and Embryology Authority in the UK, include Gamete Intra-Fallopian Transfer (Gift).
If you look at the Human Fertilisation Embryology Bill which cleared some of its major hurdles, a good bill doing good things that affects people's lives.
Trish Davies, director of regulation at the Human Fertility and Embryology Authority (HFEA), backed the strategy and said they would be monitoring clinics' performance.
The age limit for NHS-funded fertility treatment is 38 in Scotland and 39 in Northern Ireland, according to the Human Fertilisation and Embryology Authority.
BBC: IVF should be given sooner and to older women, says NICE
The Human Fertilisation and Embryology Act 1991 requires clinics to take account of the welfare of the unborn child - including the need for a father.
Although human cloning is currently banned by the Human Fertilisation and Embryology Authority, Milburn says its policy could be overturned at any time and a licence issued.
As part of the reforms to the 1990 Human Fertilisation and Embryology Act, the government intends to change the law to outlaw sex selection for non-medical reasons.
In the UK the HFEA (the Human Fertilisation and Embryology Authority) concluded that "sufficient arrangements are in place to protect the welfare of the child in these circumstances".
The vote saw MPs of all parties have a free say on the issue and were on a series of amendments to the Human Fertilisation and Embryology Bill.
At this week's meeting of the European Society for Human Reproduction and Embryology, in Berlin, research groups from America, Belgium, Denmark and South Korea announced significant progress in ovarian grafting.
The Human Fertilisation and Embryology Authority, which regulates fertility treatment in the UK, ruled earlier this year that a maximum of two embryos should be implanted in each cycle of treatment.
"They give us an unprecedented look into the very early embryology of these developing dinosaurs, " said paleontologist Mark Norell at the American Museum of Natural History in New York, who wasn't involved in the find.
Dr Takumi Takeuichi, who presented the research at the European Society for Human Reproduction and Embryology meeting in Lausanne, said that he felt it might be possible to use just about any cell in the woman's body.
While the Human Fertilisation and Embryology Authority has drawn up a list of the conditions for which it is permissible to screen, decisions as to whether to fund this on the NHS are made on a case-by-case basis at a local level.
Juliet Tizzard, policy director of the Human Fertilisation and Embryology Authority (HFEA), believes this was the right thing to do, but donor numbers have declined, and many people go abroad particularly because there is still anonymity, and many donors prefer it too.
Speaking at the European Society of Human Reproduction and Embryology conference, Dr Julie Nekkebroeck, who carried out the small Belgian study of 15 women, said they also found that 27% wanted to give their relationship a chance to blossom before bringing up the subject of having a baby.
Working in close collaboration with gynecologist Patrick Steptoe, who died in 1988, Dr. Edwards overcame entrenched political and religious hostility, as well as the disapproval of many other scientists at the time, to pioneer the basic techniques of human embryology that led to the birth of the first test-tube baby, Louise Brown, in 1978.
WSJ: Test-Tube Baby Pioneer Robert Edwards Wins Nobel Prize for Medicine
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