but I don't think it works in this case

eg. Governments have a mandated authority whether you agree with them or not, where does authority come from in Islamic jurisprudence?

Answer: from the Qu'ran and Hadith but Islamic scholars/judges still interpret them, a lay man could not do it.

The Organizations listed in the list from which the Shariah Court of Britain is made up are the foremost scholarly mainstream Muslim centres in the UK.

Therefore if they do not have any worth then no one has, and all such councils around the land should pack up shop and not bother.

Hope my thought process is clear.

I don't go to mythical places with strange men.
-- Douglas Adams, The Long Dark Tea-Time of the Soul.