Archbishop of Canterbury Rowan Williams called for "constructive accommodation" over such issues as resolving marriage disputes.
He told BBC radio that people should approach Islamic law with an open mind, while stressing there was no place for "extreme punishments" and discrimination against women in
Williams conceded that some people may be surprised by his comments, but underlined the importance of making all communities in
The issue of Muslim integration has been particularly sensitive in
Williams said: "There is a place for finding what would be a constructive accommodation with some aspects of Muslim law as we already do with aspects of other kinds of religious law."
It would be "quite wrong" to sanction a system which gave people no right of appeal, he continued, "but there are ways of looking at marital disputes, for example, which provide an alternative to the divorce courts as we understand them."
He added: "It seems unavoidable and, as a matter of fact, certain conditions of sharia are already recognised in our society".
But Prime Minister Gordon Brown's spokesman said British law must be based on British values.
"Our general position is that sharia law cannot be used as a justification for committing breaches of English law, nor should the principles of sharia law be included in a civil court for resolving contractual disputes," he said.
He noted that
"In general terms, if there are specific instances that can be looked at on a case-by-case basis, that is something we can look at," he said.
But he added: "The prime minister believes British law should apply in this country, based on British values."
Williams called on people to look at sharia "with a clear eye and not imagine, either, that we know exactly what we mean by sharia and just associate it with ... Saudi Arabia or whatever.
"Nobody in their right mind would want to see in this country the kind of inhumanity that has sometimes been associated with the practice of the law in some Islamic states: the extreme punishments, the attitudes to women."
Williams, whose comments come ahead of a lecture he was due to give Thursday night entitled "Islam In English Law", has consistently called for Christian and Muslim leaders to work together.
Background of Rowan Williams
Archbishop of Canterbury Rowan Williams is a former academic who became head of the Anglican Church in 2002.
Williams was born in the Welsh city of
He was ordained in 1977 and was a chaplain in
Two years later, he replaced George Carey to become the 104th Archbishop of Canterbury, head of a church which claims to have 80 million followers around the world.
Williams is highly respected as a theological writer, drawing on his adacemic background and supported by his wife Jane, a lecturer on theology with whom he has two children.
Williams speaks seven languages including Welsh