Lord Phillips of Worth Matravers, the Lord Chief Justice, strongly backed Rowan Williams, the Archbishop of Canterbury, over his suggestion earlier this year that aspects of sharia should be adopted in Britain.
The archbishop's remarks sparked a national debate and led to calls for his resignation.
Risking inflaming that controversy again, Lord Phillips has said that Muslims in Britain should be able to use sharia to decide financial and marital disputes.
The judge did add that only the criminal courts should have the power to decide when a crime has been committed and when to impose punishment.
But his suggestion that different religious groups should run their affairs according to different rules sparked warnings that community cohesion could be undermined.
In a speech at the East London Muslim Centre, Lord Phillips said it was "not very radical" for Dr Williams to argue that sharia can be used to help govern issues like family disputes and the sale of financial products.
Lord Phillips said: "It is possible in this country for those who are entering into a contractual agreement to agree that the agreement shall be governed by law other than English law."
Therefore, he said, he could see no reason why sharia should not be used to settle disputes in this country.
He said: "There is no reason why principles of sharia, or any other religious code, should not be the basis for mediation or other forms of alternative dispute resolution."
He added: "It must be recognised however that any sanctions for a failure to comply with the agreed terms of the mediation would be drawn from the laws of England and Wales."
Sharia suffered from "widespread misunderstanding" in Britain, Lord Phillips said.
"Part of the misconception about sharia is the belief that sharia is only about mandating sanctions such as flogging, stoning, the cutting off of hands or death for those fail to comply with the law," he said.
"In some countries the courts interpret sharia as calling for severe physical punishment. There can be no question of such courts sitting in this country, or such sanctions being applied here."
The judge said Dr Williams had been misunderstood when it was reported in February that he said British Muslims could be governed by Sharia.
Lord Phillips said that the archbishop was saying only that "it was possible for individuals voluntarily to conduct their lives in accordance with Sharia principles without this being in conflict with the rights guaranteed by our law".
There is already scope in English law for some communities to use their own religious codes to resolve disputes. Orthodox Jews can use the Beth Din rabbinical courts to decide on matters including divorce.
However some critics say that women marrying under sharia do not have the same rights as in English law, and could lead to them being treated as second class citizens as far as divorce settlements, custody of children and inheritance go.
Muslim and Christian politicians expressed fears that at a time of heightened tensions, encouraging Muslims to live by their own distinct rules could make it harder for different communities to integrate.
Khalid Mahmood, Labour MP for Birmingham Perry Bar and a practising Muslim, said that allowing sharia in parts of the UK would be divisive.
He said: "This would create a two-tier society. It is highly retrograde. It will segregate and alienate the Muslim community from the rest of British society.
"The majority of British Muslims want to live only under British law and they would reject anything that means they are treated differently.
"What Lord Phillips and the archbishop are discussing is something that is completely outside their area of understanding."
Philip Davies, the Conservative MP for Shipley, said Lord Phillips' suggestion was "totally unacceptable."
He said: "It is very unhelpful for community cohesion. This is the sort of thing that builds up tensions in areas like mine, in places like Bradford. Sharia law has got no place in any shape or form in British law."
Andrew Selous, a Tory MP and chairman of the all-party Christians in Parliament group, said calls like those made by Lord Phillips and the archbishop were "worrying."
He said: "As far as people of all faiths are concerned, it is important that we are all equal under one United Kingdom law. It will lead to more community tensions rather than less."
Lord Ahmed, a Labour peer and practicing Muslim, said there was a "big debate" among British Muslims about whether and how Sharia should apply in the UK.
He said: "There is a risk that this would make it harder for communities to integrate -- we all need to do more to integrate, and mainstream society has to do more as well."
"We should have one law for everyone in the UK, but there may be very rare occasions when exceptions have to be made, like for marriage, divorce and food."
A Muslim lawyer said that raising the prospect of allowing people to live under Sharia in Britain would "alarm" people.
Mahmud Al Rashid, spokesman from the Association of Muslim Lawyers, said: "There is massive misunderstanding about what Sharia is. It is not a single law."
A spokesman for Dr Williams said: "We welcome the speech given by the Lord Chief Justice as a positive and constructive contribution to this important and ongoing debate."
Cardinal Cormac Murphy O'Connor, the Archbishop of Westminster and leader of Britain's Catholics, said that people should live under the laws of the UK.
His spokesman said: "As the Cardinal has consistently said and indeed said earlier this year, was that Britons should abide by and be subject to the law of the land."
Downing Street said the Government's position on the issue of Sharia had been made clear at the time of the controversy over the Archbishop's speech.
"We think that British law should be based on British values and determined by the British Parliament," the Prime Minister's spokesman said.
Baroness Warsi, the Conservative shadow minister for community cohesion, backed the judge.
She said: “The Lord Chief Justice's speech is a very clear and unifying speech for our communities in Britain.
”I specifically endorse the points made by Lord Phillips that with equality of rights come responsibilities. It is absolutely essential that everyone in this country is treated equally by the law but it is important that everyone is equally subject to it, and that the same laws apply equally to everyone.”
