Based on the info you've given, it sounds reasonable to move into management consultancy. You would be best off to target niche consultancies that specialise in working with clients in the financial services sector. There are even some consultancies that specialise in working with private banking clients. In this way, you can leverage your previous experience best and have the most impact early on.
If you are thinking of consultancy as a way to broaden your experience and move away from private banking, then you could target financial services practices within larger consultancies - you can then put your experience to work but also get secondments and transfers to other teams in future.