Geraldine Smith MP said "These are matters of conscience and not party political issues."
Prime Minister Gordon Brown has been called on by Labour MPs to allow them to vote according to conscience on the Government's upcoming Human Fertilisation and Embryology Bill.
It has been expected that Labour MPs will be whipped to vote for the Government Bill, regardless of their moral objections to its contents.
The Bill contains controversial measures, including the creation of animal-human embryos for research. It could also be used to change the law on abortion.
Although Labour MPs will be allowed a free vote on abortion, they are likely to be forced to vote for the rest of the Bill along party lines.
"I am appealing to like-minded people to write to the three party leaders, urging them to allow a free vote on the bill" the Labour MP for Bootle, Joe Benton, told Roman Catholic newspaper, The Universe.
Labour MP for Morecambe and Lunesdale, Geraldine Smith, added: "These are matters of conscience and not party political issues."
There have also been calls for the Bill to be re-drafted in light of recent advances that make the use of animal-human hybrid embryos unnecessary for medical research.
The recent breakthrough in reprogramming adult skin cells to behave like embryonic stem cells promises "a plentiful new source of stem cells for research into new treatments for diseases such as Alzheimer's and Parkinson's", says Dr. Calum MacKellar, Director of Research of the Scottish Council on Human Bioethics.
Crucially, the new source of stem cells comes from adult skin cells, and so bypasses the ethical problems of creating, using and destroying animal-human embryos in research.