There are over 50 sharia courts in the UK, they have no legal authority but they do have authority in communities. My niece is a Muslim and married a Muslim man. They had their Nikah ceremony and never registered the marriage so she has no marriage rights. That doesn't matter now but what happens if something goes wrong one day?
If the worse happened and she ever wanted to get a divorce then she'd have to go to a shariah court and follow Islamic rules to grant the divorce. The most notable thing for divorce is the husband must grant it, what if he doesn't? She could then just ignore it given the marriage wasn't ever legal but think of everything that entails and the impact. She could essentially be ostracised within her community.
The government hides behind what you have just said. Yeah it isn't part of the legal system but let's not pretend that it isn't being practiced and doesn't pose a huge problem, especially for women who are especially isolated by Islam. I am not Islamaphobic but I am certainly suspicious of a religion which enforces itself through religious law and clearly with little regard to the actual law.