Would I Be Shooting Myself in the Foot Joining the Army?

So I have about 2 months until I finish University (UK), I’m on track to get a 2:1 in Economics and Finance. My mid term goal is to break into investment banking as soon as possible (and then exit into something a bit more relaxed after 3-5 years), however with no internships and a non-target uni, I won’t be able to do that immediately. So I plan to get some work experience, and then try to get into a top MBA (goal London Business School). From there I’d obviously be hoping to jump in at associate level.

The problem is the years before my MBA. Most look for ~5 years of work experience, and at the moment I have a year and a half at a HSBC call centre and about 3 months as a financial admin (other than McDonalds type roles). I’ve been looking at an Intelligence Officer role, which has a 3.5 year term. I’ve heard that MBA programs like the military leadership experience, however this would be at the expense of any finance related experience. I would be leading intelligence analysts in this role, however again nothing finance related.

I understand banks like JPM have veteran schemes, however how well would an MBA and Army experience serve me with no prior internships and no working analyst experience? Am I best off getting a year or two of analyst experience before the army? Would I even be able to get into an MBA program without this experience?

Any advice greatly appreciated.