Rowan Williams told BBC 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.
He says that 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".
Dr Williams said there was a place for finding a "constructive accommodation" in areas such as marriage - allowing Muslim women to avoid Western divorce proceedings.
Other religions enjoyed such tolerance of their own laws, he pointed out, but stressed that it could never be allowed to take precedence over an individual's rights as a citizen.
His "cure"? Well, our "perception" of Sharia law must change.
He said people needed to look at Islamic law "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."
I'm sorry... but I must be missing something. Is there another, kinder-gentler Sharia law in existance somewhere that doesn't require women being put to death for adultry? Whipped for appearing with other men in public? Refuses education to female youth? Forbids contact with certain western cultural phenoms?
Is this guy kidding? Or just unbelievably stupid?
Nations thrive when there is unity and pride in their national kinship and shared laws. The biggest problems Europe has - most especially the Netherlands and France - is the fact that the Muslim immigrant population refuses to integrate.... to be part of the nation they migrated to. This is diversity to the extreme, and leads only to a nation torn asunder.
The Archbishop calls for an act that will be the beginning of the end for GB as the world knows it. Having two separate justice systems based on religion will create islands of stateless denizens that do not interact, nor care about the well being of their neighbors. His notion of a utopian "cohesion" is more than seriously flawed... it's downright dangerous. It is, in fact, handing a Caliphate, sans protest, to Muslim militants.