Leading politicians have distanced themselves from the Archbishop of Canterbury's belief that some Sharia law in the UK seems "unavoidable".
Gordon Brown's spokesman said the prime minister "believes that British laws should be based on British values".
The Tories called the archbishop's remarks "unhelpful" and the Lib Dems said all must abide by the rule of law.
Dr Rowan Williams said the UK had to "face up to the fact" some citizens do not relate to the British legal system.
He said adopting parts of Islamic Sharia law could help social cohesion.
For example, Muslims could choose to have marital disputes or financial matters dealt with in a Sharia court.
But the prime minister's official spokesman said Sharia law could never be used as a justification for committing a breach of English law, nor could the principle of Sharia law be applied in a civil case.
He added that Mr Brown had a good relationship with the archbishop, who was perfectly entitled to express his views.
All British citizens must be subject to British laws developed through Parliament and the courts
Sharia law in the UK
Religious courts already used
Home Office Minister Tony McNulty said: "To ask us to fundamentally change the rule of law and to adopt Sharia law, I think, is fundamentally wrong."
And Culture Secretary Andy Burnham told BBC One's Question Time: "This isn't a path down which we should go.
"You cannot run two systems of law alongside each other," he said, adding this would be "chaos".
For the Conservatives, shadow community cohesion minister Baroness Warsi said the archbishop's comments were "unhelpful".
"Dr Williams seems to be suggesting that there should be two systems of law, running alongside each other, almost parallel, and for people to be offered the choice of opting into one or the other," she told BBC News 24. "That is unacceptable."
Liberal Democrat leader Nick Clegg said he had "an enormous amount of respect" for Dr Williams, but could not agree with him on this issue.
"Equality before the law is part of the glue that binds our society together. We cannot have a situation where there is one law for one person and different laws for another.
"There is a huge difference between respecting people's right to follow their own beliefs and allowing them to excuse themselves from the rule of law."
Trevor Phillips, who chairs the Equality and Human Rights Commission said the "implication that British courts should treat people differently based on their faith is divisive and dangerous".
"It risks removing the protection afforded by law, for example, to children in custody cases or women in divorce proceedings," he said.
"There is a fundamental principle here when you appear before a court in Britain you appear as a citizen, equal to any other and you should be treated equally to any other."
Dr Williams said Muslims should not have to choose between "the stark alternatives of cultural loyalty or state loyalty".
In an interview with BBC correspondent Christopher Landau, he argued this relied on Sharia law being better understood. At the moment, he said "sensational reporting of opinion polls" clouded the issue.
He stressed that "nobody in their right mind would want to see in this country the kind of inhumanity that's sometimes been associated with the practice of the law in some Islamic states; the extreme punishments, the attitudes to women as well".
But Dr Williams said an approach to law which simply said "there's one law for everybody and that's all there is to be said, and anything else that commands your loyalty or allegiance is completely irrelevant in the processes of the courts - I think that's a bit of a danger".
"There's a place for finding what would be a constructive accommodation with some aspects of Muslim law, as we already do with some other aspects of religious law."
Dr Williams added: "What we don't want either, is I think, a stand-off, where the law squares up to people's religious consciences."
"We don't either want a situation where, because there's no way of legally monitoring what communities do... people do what they like in private in such a way that that becomes another way of intensifying oppression inside a community."
Under English law, people may devise their own way to settle a dispute in front of an agreed third party as long as both sides agree to the process.
Muslim Sharia courts and the Orthodox Jewish courts which already exist in the UK come into this category.
Mohammed Shafiq, director of the Ramadhan Foundation, welcomed Dr Williams's comments, saying they "further underline the attempts by both our great faiths to build respect and tolerance".
He added: "Sharia law for civil matters is something which has been introduced in some western countries with much success. I believe that Muslims would take huge comfort from the government allowing civil matters being resolved according to their faith."
Ibrahim Mogra, of the Muslim Council of Britain, said: "We're looking at a very small aspect of Sharia for Muslim families when they choose to be governed with regards to their marriage, divorce, inheritance, custody of children and so forth."
He added: "Let's debate this issue. It is very complex. It is not as straight forward as saying that we will have a system here."
But Mark Pritchard, Tory MP for the Wrekin, in Shropshire, said the archbishop's comments were "naive and shocking" and he accused him of "pseudo-theological appeasement".
He said: "The archbishop should be standing up for our Judeo-Christian principles that underpin British criminal law that have been hard fought for.
"He should be concentrating on winning souls into the Church of England rather than getting involved in politics."