Career Change with MBA in UK?

Hello all,

In the next couple of years I'm looking to do an MBA for a career change into banking, I currently work in hospitality and am at a manager's level. I know I would be a complete wildcard with an attempt to break into banking from a non-finance background and most of my experience being in hospitality but I'm wondering whether there's a chance? I would be doing the MBA either way as it's helpful in hospitality if I choose to stay on my current path.

As I'm looking at working in London, although WS isn't off the table if I can get there, I'm thinking of applying for Oxbridge and LBS or going stateside to HBS, Wharton or Columbia. The only downside in applying that I see currently is that I'm doing an OU undergrad degree which is distance learning and whether I'd be able to go straight into an MBA despite having plenty of experience behind me.

How much of a disadvantage am I at due to my current educational route and work background with regards to getting into banking?

Any advice welcome :)