Rowan Williams, the Archbishop of Canterbury, has made admirable efforts to engage constructively with Islam and its clerics. His sensible conversations about the Muslim world stand in welcome contrast to the attitude of some of his colleagues, notably the Bishop of Rochester, whose remarks last month about unspecified “no-go areas” for non-Muslims were unnecessarily provocative. Many members of the Church of England were furious, and felt that those remarks undermined all the work they had been doing to improve interfaith relations.

In trying to retrieve that situation, and smooth sensibilities, Dr Williams did something yesterday that was far from sensible. He said that the adoption of parts of Sharia in Britain looked “unavoidable”, and called for “constructive accommodation with some aspects of Muslim law”, over issues such as resolving marriage disputes. Muslims should not have to choose, he said, between “the stark alternatives of cultural loyalty or state loyalty”.

These remarks are astonishing. Because a different set of rules seems “more appropriate ... in some cultural and religious settings” does not justify exempting one set of citizens from the laws laid down by Parliament. It is fundamental to this democracy that there should be one law for everyone. People of many faiths - Jews, Hindus, Sikhs - have settled happily in Britain without demanding a new set of laws for themselves. It would be more useful to ask how to help more Muslims to integrate successfully into what is a tolerant culture, than to urge a change in that culture to suit a notion that some parts of the Muslim community feel more comfortable with.

It is not clear how far the Archbishop is suggesting that Sharia should apply. He has certainly denounced its more extreme forms. It is also clear that Sharia differs widely in its application from country to country. But that is not really the point. In Britain, all citizens are equal before the law. Anything that might skew that balance ought to be wholly unacceptable.

In 2001 the European Court of Human Rights stated that Sharia clearly diverged from the human rights values enshrined in the European Convention. In 2005 concerns about human rights and women's rights led to a storm of protest in Canada, when the attorney-general of Ontario proposed to adopt Sharia-based law to settle Muslim family disputes over divorce and child custody. The proposal was quashed on the grounds that there should be one law for all Canadians, amid fears that Islamic tribunals could lead to discrimination against women.

Dr Williams may be unaware of the Canadian experience. But while his desire to reduce what he calls “social suspicion” is genuine, his way of going about it seems guaranteed to create even more suspicion and hostility. The established Church was founded to break from the parallel jurisdiction in Rome. It is extraordinary to hear the head of the established Church, 500 years later, argue for a return to a parallel jurisdiction for another faith. We all wish to live in harmony. There are important questions to be answered about how to make Muslims feel more welcome in British society. But this is an act of appeasement. It threatens to undermine the practice of all faiths in Britain and the strength of our parliamentary democracy.