Lord Phillip's words make this clear:
"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."
If you want Sunni law to apply, you can choose to apply Sunni law rather than English law. If you want Shia law, you apply Shia Law.
As he describes, a contract would legally bindingly set the code of law under which a divorce would be handled. So if a woman and her husband both specify when signing the marriage that divorce should be handled according to Islamic law, she will be bound by that. She can't change her mind later - the governing law is specified as the contractual agreement is entered.
I think that you may be one of those people who Lord Phillips refers to as misunderstanding Shariah law. Give in to the Lord's wisdom :)
So there will be multiple versions of Sharia law, one for Shia, one for Sunni, one for Ahmedis and one for some other sect? All clauses will be written down in the nikah contract initially, and then if a divorce happens, those clauses will be referred to? If a clause wasn't written down, I am assuming a mufti will be consulted with. if so what kind of Mufti? A "Mod Muslim" mufti, or one with a more traditional outlook?