Sharia courts in Britain are onl permitted under certain circumstances, if both parties agree and if the matter at hand does not necessarily require the involvement of the courts. In your scenario, there would be no question. It would go through the British court system, which, by the way, is secular, not Christian.

The British Legal System is not based on religion - if it were a criminal case to be heard in Britain it would be subject to the Criminal Justice System and progressed through the British Courts. Sharia courts are not comonplace in Britain and in my opinion shouldn't be considered in criminal cases at all, which thankfully remains the case at present.

Point 1, which others have made, is that British law is secular. Historically it has been based upon Christian values, but neither the law nor the courts promote Christianity. In a criminal trial, the case would be heard in a magistrate or crown court. Sharia courts can be consulted in these cases, but they have no jurisdiction - they are consulted to provide testimony if it is relevant to the conduct of a defendant. For example, if a defendant claims they acted in accordance with sharia law, a sharia court may be consulted. This is not to make a judgement on the case, but to provide testimony, in the same way other expert witnesses are brought in to examine the other claims of both the defense and prosecution. In effect, they are a cultural reference. In a civil case, one is not required to settle in court, the courts are there as an option to provide arbitration according to the law. One may also settle disputes out of court or using dispute procedures set down by sharia law, or jewish law, or any other system: as long as both parties willingly agree, an agreement or judgement may be reached. Her Majesty's Court Service exists to provide people with a system they can always turn to, but for civil cases does not require them to turn to it.