The scientists who cloned Dolly the sheep are applying for a licence to clone human embryos.
Professor Ian Wilmut, of the Roslin Institute in Edinburgh, wants to use cloned human embryos to study motor neurone disease (MND).
His application to the Human Fertilisation and Embryology Authority is expected to provoke criticism that testing human embryos is immoral.
Therapeutic cloning for research has been legal in the UK since 2001.
It is designed purely for research. Professor Wilmut has stressed that his team has no intention of producing cloned babies, and said the embryos would be destroyed after experimentation.
He told the BBC: "Because at this early stage the embryo does not have that key human characteristic of being aware to me it would be immoral not to take this opportunity to study diseases."
Until recently, Professor Wilmut had said he would not work with human embryos.
MND is caused by the death of cells - called motor neurones - that control movement in the brain and spinal cord.
It affects about 5,000 people in the UK. Half of people with MND die within 14 months of diagnosis.
Weakness in the muscles that supply the face and throat also cause problems with speech and difficulty chewing and swallowing.
Professor Wilmut has applied for a licence
The aim is to study what goes wrong in the nerve cells of patients suffering from MND.
Professor Wilmut's team plan to take DNA from the skin or blood of a person with MND and implant it into a human egg from which the genetic material has been removed.
The egg would then be stimulated to develop into an embryo.
The scientists would remove cells from the embryo while it was still in the earliest stages of development, and study them to gain a better understanding of the disease. The embryo would be destroyed while still just a few days old.
If successful, Professor Wilmut said the technique could have profound implications for a range of other debilitating neurological and genetic disorders.
His team is the first to apply for a therapeutic cloning licence in the UK.
However, it is less than three months since scientists in South Korea announced that they had created 30 cloned human embryos for research purposes.
Difficult to study
Dr Robin Lovell-Badge, head of developmental genetics at the National Institute for Medical Research, said MND, along with many other diseases, was difficult to study in patients.
"By the time you get to them they are already sick, and it is unethical to do much then."
He said Professor Wilmut would be testing embryos that were just a ball of a few hundred cells at a stage long before any development of a nervous system.
However, Patrick Cusworth, a spokesman for the charity Life UK, voiced opposition to the research.
He said: "It comes as no surprise that Professor Wilmut has decided to extend cloning from animals to human beings.
"The fact that he does so under the banner of so-called therapeutic cloning makes no difference whatsoever to the fact that a human being is being deliberately created and then destroyed."
Mr Cusworth said alternative techniques - such as taking samples from umbilical cord blood - were available to allow scientists a supply of cells for experimentation without having to go down this line.
Fertility expert Lord Winston argued that all cells had the potential for human life.
"I don't think that changes the argument that actually it is a moral duty to try to enhance, protect and promote healthy human life - which is exactly what this project is trying to do."
George Levvy, chief executive of the MND Association, said the research had the potential to "revolutionise the future treatment of MND".
He said: "The Association recognises that the issues of embryonic stem cell research and therapeutic cloning raise significant moral, ethical and religious concerns.
"However, in principle we will support this research project, as long as we are satisfied that it is legal, has a sound scientific rationale and has the potential to bring us closer to treatments and/or a cure for MND."