Your entire comment about a murder victim was a strawman. And not the first such one on this thread. To do that would be to have a two tier, immoral unfair system. It's not at all what the archbishop was on about.
But some people hear the words Sharia and immediately assume he's saying that Muslims in the UK should be able to behead people.
It's actually pretty sad that even on a board which is supposed to be devoted reasoned discussion of a subject that people can't be bothered to actually figure out what the man was saying before saying he's wrong to say it. 
Don't try to tell me what my comment was or wasn't when you clearly don't have the foggiest of where I'm coming from. (Either that, or you're intentionally misunderstanding me...

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I did read the news article you posted, and I saw very little that was relevant to the current discussion; the article did not discuss what would end up being changed at all.
For that matter, I never stated that he was wrong to say it.

All I did was express the views that I felt were pertinent. I never passed judgments on the statements or on the proposed changes, I simply stated what I agreed with and what I didn't agree with, in extremely generalized terms.
If you expect a reasoned discussion on the subject, you need to actually try to understand what people are saying, rather than jump to conclusions and stuff words in people's mouths. There is
no way to have a reasonable discussion when I say that exploiting legal loopholes to get a lighter penalty for murder is wrong, and you respond by acting as if I'm saying that freedom of speech needs to be oppressed.
I don't have any clue what, exactly, the archbishop was suggesting would be added beyond "Civil codes", and I don't think anybody in this thread knows anything any more concrete than that. Hell I doubt he himself knows exactly what that would mean; it sounds more like an off-the-cuff opinion based on his knowledge and research, rather than a coherent plan of action to integrate Sharia civil codes into British legal infrastructure. So I don't see why you're going out of your way to accuse people of being just short of ignorant bigots for stating their general opinion on the subject, when nobody at all is qualified to discuss the specifics.
Given the liberal leaning of this board, I'd imagine that most people
wouldn't be opposed to third-party arbitration for disputes that really only involved two people. But I think you'll find that there are a lot of 'private' disputes whose resolution would have an impact on non-Muslims, but who wouldn't technically be part of the case. If a business or a business owner is involved, what say do his customers get? If a man takes his wife to court for infidelity, does the lover get any say? What if Sharia civil code demands that the lover suffer some penalty? What if the religious civil code requires a punishment that's in violate of British law? What if someone is essentially forcced into attending the court based on social pressure? What if someone is treated unfairly because the system does not have the same built-in protections against abuse as the British judicial system (What those safeguards might be, I don't know).
What if the case involves a minor?
The key problem is that the reason behind setting the new laws into motion is that they would conflict with the legal system today. If that's true, you've basically got the state contradicting itself on the basis of religion - which doesn't seem fair at all. (Who gets to use the courts? Why do Muslims get their own court but not anyone else? Etc etc.)
Rewrite 'court' with 'third-party arbitration' if you see it as more appropriate. But so long as it operates due to a consistent set of rules, and acts like a court, and has the same authority as a (low-level) court, I don't see how you can claim that it's radically different from, well, what it is. For marital issues, it does make some sense, or at least it would if the situation is like here in the States - where the church has a strong influence over the institution of marriage (Maybe too strong - but that's another discussion entirely).