Here are the sharia-compliant ones I know of (there may be others...)

Abu Dhabi Islamic Bank
Al Rayan Bank
Bank of London and The Middle East Gatehouse Bank
QIB UK

According to the rule of law in the UK, sharia principles for settling disputes, etc., may be applied only if all parties involved give consent. Sharia principles may not be used to override UK law.

Them's the rules and I know that in most walks of life rules may be bent or broken. As has been indicated, the banking sector is tightly regulated.