You can do your thesis on Islamic Finance in general across all universities in uk, as long as someone is willing to supervise you. I know people who have done PhDs on Islamic finance related topics from Southampton, Brunel, hull, Manchester, Bradford, queens.. To name few.
Look for faculty who are willing to supervise regardless of any particular university
For the list of all global universities including UK offering education and scholarships in Islamic finance, follow this single resource for the admission links of all the universities. I hope it helps.