Let's be clear: RC canon law and Jewish courts granting divorces and so on are NOT the same thing as what the Archboob was talking about. In a State governed by its own organic law, RC canon law, Jewish divorce courts, the membership discipline of the local Masonic lodge or Boy Scout Council, are all in the nature of private voluntary agreements. The official stuff is all in the law code, including marriage and divorce. There is one law for everybody. If you also want your marriage recognized by your Church (or your marriage recognized as dissolved by your Church), if you want somebody thrown out of your club for breaking an oath to you, yada yada yada, then more power to you. But the only compulsion exercised upon parties to such proceedings is that of peer pressure: as long as you want to belong to Group X in good standing, you have to do it their way. If belonging to Group X doesn't matter to you, you can stick your tongue out at them and go on your merry way.
Here's the deal: the State does not enforce the decrees of these social organizations' machinery. If the State has granted you a divorce, but the RCC says you are still married, any RC can contract a second legal marriage. He (or she) may forfeit all kinds of things, including his good standing in the RCC, but if those don't matter to her, so what? But the advocates aren't asking for sharia in that form. They have that already. What they want is for the law of the State to allow religious law to trump State law.
One result of this would be to abandon the many women who want safely out of abusive marriages to the tender mercies of a misogynistic legal authority. Now, if they want to live under that authority, they're welcome to; but, they have that right now. OTOH, if they want out, the law of the State should protect them and let them follow their own course.
So, what the Archbishop has advocated is an absolutely terrible idea. It's not a means of including Muslims in a multicultural UK; rather, it's a means of denying some Britons the protection of equal justice under law. Personally, I think it's time for the good bish to retire.