A new network of courts in five major cities is hearing cases where Muslims involved agree to be bound by traditional sharia law, and under the 1996 Arbitration Act the court's decisions can then be enforced by the county courts or the High Court.
Officials behind the new system claim to have dealt with more than 100 cases since last summer, including six involving domestic violence which is a criminal rather than civil offence, and said they hoped to take over growing numbers of 'smaller' criminal cases in future.
http://www.dailymail.co.uk/news/article-1055764/Islamic-sharia-courts-Britain-legally-binding.html
These people think they do.
Those arbitration courts are subject to British law not equal to it.