The group, led by Bill Cash, a senior Tory backbench MP, includes former ministers, Labour MPs and Liberal Democrats. The the motion calls for an ad hoc committee of MPs to carry out the investigation.
"A inquiry is needed in the interests of our constituents and the nation as a whole. It is crystal clear that what is being done is being monitored by scientists. They are not elected and these questions are so important that the issues have to be thoroughly investigated by lay people, with the facts brought out on the table, not kept behind closed doors," Mr Cash said.
The possibility of the cloning of humans topped the agenda at the first meeting yesterday of the Human Genetics Advisory Commission. But the nine members decided only to check that existing UK laws are adequate to prevent it happening here.
Cloning of human embryos by nuclear transfer - the technique used to produce Dolly the sheep - is already expressly forbidden by the 1990 Human Fertilisation and Embryology Act.
Sir Colin Campbell, the commission's chairman, said "There is no doubt that genetics will continue to be a major issue."
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