This issue runs far deeper than to simply suggest that Sharia Courts are merely a form of arbitration. It might be argued that a Sharia Court is a “properly convened tribunal” under the Arbitration Act which Corby mentions. However, I doubt it. I won’t bore readers with details from all 110 Sections and four Schedules from the Act. But two sections are worth particular mention. The introduction sets out general principles:
"The provisions of this Part are founded on the following principles, and shall be construed accordingly—
(a) the object of arbitration is to obtain the fair resolution of disputes by an impartial tribunal without unnecessary delay or expense;
(b) the parties should be free to agree how their disputes are resolved, subject only to such safeguards as are necessary in the public interest;
Note (a) “.. to obtain the fair resolution of disputes by an impartial tribunal..”. It is unlikely in the extreme that a Sharia Court arbitrating on family and matrimonial matters (of the type mentioned in this question) would be fair or likely to act impartially. For a start, because of the male centric setup of the Sharia system (and Islam in general) no females will be involved. Secondly, it will rule in accordance with Islamic principles where women are decidedly second class citizens (if indeed they are even afforded that status) and a fair resolution would thus be impossible.
Then consider (b) “the parties should be free to agree how their disputes are resolved,…”. Women will have no say how such disputes are resolved. They will be told (by their male relatives) that the matter will go to the (male dominated) Sharia Court.
This feeds smoothly into Section 16 which describes the procedure for appointment of arbitrators. Here it states that each of the arbitrees will contribute equally to the choice of composition and selection of the arbitration panel. There is no way on earth that Muslim women appellants will have any say in such matters. I would suggest that on these two bases alone Sharia Courts do not comply with the 1996 Act.
However, all that is largely beside the point. The UK has a perfectly robust and mature system of dealing with family and matrimonial disputes based on copious statutes and case law precedents. Not perfect, I will agree, but certainly not one that discriminates enormously against half the participants simply on the basis of their gender or one which is presided over exclusively by men.
To suggest that Muslim women “agree” to be bound by decisions made by Sharia courts is simply laughable. They have no say in the matter; they have none of the usual safeguards that participants in court proceedings have; there is no control over fairness or compliance with UK legal principles ; Sharia courts are not monitored or regulated to ensure their impartiality (indeed, if they were, they would quickly be banned as they clearly contravene much of the UK’s equality legislation.
In short they have no place in the UK and nor, for that matter, does Islam.