I don't think the Archbishop envisaged stonings, amputations and floggings for UK Moslems. Nor would he advocate polygamy or the compulsory wearing of a headscarf. The sharia is a code which is open to interpretation; not all Moslem countries apply sharia in their legal system, but of those that do, only a very few - and, I have to say it, the most backward - apply the harshest penalties.
That said, a Common Law legal system which treats all people as more or less equal will be severely undermined if new, alien, standards are introduced which apply to just one section of the population, especially where rights of appeal are limited or non-existent, and where the value of evidence given by women is half the value of evidence given by men.
I learn that Canada tried to introduce Islamic Law into matrimonial disputes between Moslems, but that these attempts were crushed by Moslem women's groups for reasons such as this.
That said, although the British legal systems are predominantly secular nowadays, they do already recognise the binding application of Canon Law within the Church, and Rabbinical Courts for matters affecting the Jewish faith. But these laws and courts are primarily for the administration of ecclesiastic/rabbinical matters rather than governing private individuals' everyday personal affairs.
Nevertheless, there are inequalities that exist here that seem to bear most heavily on the Moslem population. For example, it used only to be possible, in England & Wales, to be married by a Registrar of Marriages except where the wedding took place in a church belonging to the Church of England. My wife is Catholic: we had to invite a registrar to attend our wedding so that it would be "legal". But my wife would not have felt properly "married" if she hadn't had a full nuptial Mass.
I understand that nowadays all Christian priests and ministers, and Jewish rabbis too, have the "civil" power to marry people, but I also believe immans do not have such powers.
Nevertheless, voluntary "Sharia Councils" exist and are permitted which already deal with matrimonial mattters, and, once they decide an issue, the parties concerned rarely try to enforce their legal rights to override that decision.
There are many other issues, too, and I fear I have oversimplified the ones I have discussed. The matter is highly complex.
However, I believe that, on balance, the established law of the land must always prevail, and while cultural differences can be accomodated, this must not be at the expense of anyone's rights and liberties.
TYWD