The interview is currently available on the BBC's The World at One site.
The Archbishop of Canterbury says the adoption of Islamic 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 some aspects of 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".
An approach to law which simply said - there's one law for everybody - I think that's a bit of a danger
Dr Rowan Williams, Archbishop of Canterbury
In an exclusive interview with BBC correspondent Christopher Landau, ahead of a lecture to lawyers in London later 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; states; the extreme punishments, the attitudes to women as well".
But Dr Williams says the argument that "there's one law for everybody... 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 adds: "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."
His comments are likely to fuel the debate over multiculturalism in the UK.
Last month, one of Dr William's colleagues, the Bishop of Rochester, said that non-Muslims may find it hard to live or work in some areas of the UK.
The Right Reverend Dr Michael Nazir-Ali said there was "hostility" in some areas and described the government's multicultural policies as divisive.
He said there had been a worldwide resurgence of Islamic extremism, leading to young people growing up alienated from the country they lived in.
He has since received death threats and has been placed under police protection.
Source: BBC (English), h/t UP Pompeii