What he says here is no different than contract laws in Texas.
Lord Phillips said: "It is possible in this country for those who are entering into a contractual agreement to agree that the agreement shall be governed by law other than English law." ...
... He said: "There is no reason why principles of Sharia law, or any other religious code, should not be the basis for mediation or other forms of alternative dispute resolution."
This is a subset of the law for a contract that two people want to enter.
It's not to say that stoning or polygamy are suddenly ok.
It’s a foot in the door. Sharia is not just some special rules for contracts. It isn’t even just a legal system. It’s a legal and political system that dictates how all of society must be ordered. Those who want Sharia inevitably will demand it to be applied to other areas than just finance or contract laws.
I heard the conservative shadow Minister of Defense talking to Dennis Prager the other day. His reaction was (to paraphrase), “It’s nonsense. There has to be one law in Britain, British law. If people come to Britain they agree to live by British law. If not they should leave.”
Such as what? Fathers and brothers being required to kill daughters/sisters who are in the company of males without supervision? Husbands divorcing wives by saying "I divorce thee" three times?" Women completely subservient to men? Forced to wear burkas? Exactly what kind of "family disputes" is he talking about?