The Archbishop of Canterbury says the adoption of certain aspects of Sharia law in the UK "seems unavoidable".
Dr Rowan Williams told Radio 4's World at One that the UK has to "face up to the fact" that some of its citizens do not relate to the British legal system
Dr Williams argues that adopting parts of Islamic Sharia law would help maintain social cohesion.
For example, Muslims could choose to have marital disputes or financial matters dealt with in a Sharia court.
He says Muslims should not have to choose between "the stark alternatives of cultural loyalty or state loyalty".
In an exclusive interview with BBC correspondent Christopher Landau, ahead of a lecture to lawyers in London on Monday, Dr Williams argues this relies on Sharia law being better understood.
At the moment, he says "sensational reporting of opinion polls" clouds the issue.
He stresses 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."
The issue of whether Catholic adoption agencies would be forced to accept gay parents under equality laws showed the potential for legal confusion, he said.
"That principle that there is only one law for everybody is an important pillar of our social identity as a western democracy," he said.
"But I think it is a misunderstanding to suppose that means people don't have other affiliations, other loyalties which shape and dictate how they behave in society and that the law needs to take some account of that."
'Custom and community'
Dr Williams noted that Orthodox Jewish courts already operated, and that the law accommodated the anti-abortion views of some Christians.
"The whole idea that there are perfectly proper ways the law of the land pays respect to custom and community, that's already there," he said.
People may legally 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 Jewish Beth Din which already exist in the UK come into this category.
The country's main Beth Din at Finchley in north London oversees a wide range of cases including divorce settlements, contractual rows between traders and tenancy disputes.
Dr Williams' comments are likely to fuel the debate over multiculturalism in the UK.
Last month, the Bishop of Rochester, the Right Reverend Dr Michael Nazir-Ali, said some places in the UK were no-go areas for non-Muslims.
Dr Williams said it was "not at all the case that we have absolute social exclusion".