The Archbishop of Canterbury's backing for some aspects of Sharia law in the UK failed to meet the approval of the Bishop of Oxford yesterday.
Dr Rowan Williams said the UK had to "face up to the fact" some citizens did not relate to the British legal system.
The Rt Rev John Pritchard, the Bishop of Oxford, said: "I don't have a detailed understanding of Sharia law or how uniformly it is applied from country to country. Clearly we hear most about the extremes.
"But my instincts are that we should be extremely cautious about welcoming Sharia law into Britain.
"British law has been built upon Judaeo-Christian foundations over many centuries and established through Parliament and our courts and I don't think that should be undermined.
"British law ought to apply to everyone in Britain, Muslim or not."
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."
Raghib Ali, a spokesman for Oxford Muslim Community Association, said: "The principle of allowing Muslims, Jews and Christians to follow their own religious law in civil matters, such as marriage, has already existed for many years and in no way means that Sharia law is being imposed on this country."
The Rt Rev James Jones, the Bishop of Liverpool, who is also the chairman of trustees at Wycliffe Hall, one of Oxford's theological colleges, has caused controversy with his book, A Fallible Church, which questions whether Jesus was a homosexual.
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