Critics have expressed horror about research to create a human embryo with genetic material from three parents.
The aim is to get healthy offspring free of inherited genetic disorders
The Human Fertilisation and Embryology has reversed its ban on the controversial proposal from the University of Newcastle.
The researchers will transfer genetic material created when an egg and sperm fuse into another woman's egg.
The groundbreaking work aims to prevent mothers from passing certain genetic diseases on to their unborn babies.
Such diseases arise from DNA found outside the nucleus, and thus inherited separately from DNA in the nucleus.
They are collectively called mitochondrial diseases.
Mitochondria are small complex structures, which exist in every cell of the body, except red blood cells. They are responsible for producing the energy that we need to grow and live.
One unique feature of mitochondria is that they have their own DNA - mitochondrial DNA, which is inherited from the mother only.
If this DNA is faulty, a mitochondrial diseases occurs. At present, no treatment for mitochondrial diseases exists.
Studies in mice show it is possible to prevent the transmission of mitochondrial disease by moving the pronuclei - the genetic material which will go on to form a nucleus - from a fertilised egg containing bad mitochondria and putting it into another fertilised egg which only contains good mitochondria.
Professor Doug Turnbull, professor of neurology at Newcastle University, and Dr Mary Herbert, scientific director of Newcastle Fertility Centre at the city's Centre for Life, now plan to do the same in humans.
US scientists at the Institute for Reproductive Medicine and Science of St Barnabas, New Jersey, reported back in 2001 that they had successfully done similar, giving rise to 15 healthy children who appeared to be free of their mothers' disease.
Instead of transplanting the pronuclei, these researchers injected another woman's ooplasm - the substance inside the cell that contains the mitochondrial DNA and bathes the nucleus - into the egg cell of the mother with faulty mitochondrial DNA.
The UK research, funded by the Muscular Dystrophy Campaign, will check that transplanting the pro-nuclei works and is safe.
The resulting egg would never be allowed to develop into a baby.
But even if it did, the offspring would still resemble their mother and father because the mitochondrial DNA does not dictate things like hair colour.
The researchers stress that this research is only the very first step in a very difficult process, which they hope will lead to techniques that might prevent the transmission of mitochondrial DNA disease.
About one in 5,000 children and adults are at risk of developing a mitochondrial disease.
The group of conditions Professor Turnbull's team will look at is called mitochondrial myopathy.
These cause muscle weakness and wasting, making it difficult for those who have it to move normally - some may need to use a wheelchair.
The Muscular Dystrophy Campaign said it was delighted that the HFEA had given approval for the research project.
Head of research Dr David Harrison said: "The innovative approach being tested by Professor Turnbull may lead to a treatment for mitochondrial myopathies, a group of conditions that dramatically affect quality and length of life."
The public are currently being consulted about their opinions on laws governing embryo research such as this.
Some believe it is dangerous and unethical to carry out such work on human embryos and cells.
Josephine Quintavalle from Comment on Reproductive Ethics said she was horrified.
"This shows once again that the HFEA does not have any regard for public consultation and the views of the public.
"It is undesirable to create children in this way. It will shock the world. This is playing around with early human life."
Matthew OżGorman, for the charity LIFE, said: "This decision is utterly unethical, abhorrent and contrary to public opinion.
"The HFEA are relentlessly imposing their libertarian agenda on the people of this country against their wishes: the government must act to disband it immediately."
Professor Turnbull said they were not radically altering an embryo's DNA.
"We are simply changing the energy source."
Professor Azim Surani, professor of physiology and reproduction at Cambridge University, said: "I see few ethical problems as we are dealing with the embryo at a very early stage where the cells haven't even started to divide yet."
Dr Andy Miah, ethicist at Paisley University, said: "Many of the more controversial ethical concerns arise only if we project into the future and imagine that a child were to be born, as a result of this kind of procedure.
"Even if a child were born with 'two mothers', I doubt very much that we should be concerned about its welfare any more than we are concerned about the welfare of all children."