I haven't gone through the London office's interview process, but have interacted with people from the UK office. The interviews are usually the same as any other country - cases and fit interviews.
1. More often than not, they start with a personal fit interview. This can go deep depending on who is interviewing you. So, be thoroughly prepared with your CV and back-stories
2. The second / third rounds will be short and long cases. These will be typical business cases that we encounter in an MBB case interview.
3. If you are part of a large candidate group, then there may be additional group case interviews. These are also combined with a creative round (tackling a given situation/ role play etc.) or a presentation to Partner. Either way, if the number of candidates is high, you may have to be prepared for some group activities as well.
However, if the applying cohort is small, the final round will be a Partner interaction. He will have basic fit questions and might throw up a small caselet to brainstorm with him.
All the best for your interview.