I've not yet been tempted to work for them (well not tempted enough) but I've had the privilege of working with AAIB on a number of occasions.
AAIB inspector is not an entry-level job, they recruit Engineers who are at IEng or CEng level, or ATPLs with a lot of experience. In practice, many of the ops inspectors seem to have a good grasp of Engineering, and almost all of the engineering inspectors have at-least CPL level flying knowledge and experience, if not the actual license. That is what you're looking for here, if you are pre-PPL and lack at-least an Engineering degree then although I'd say it's a thoroughly worthy aim, it's not going to happen next year.
Without doubt they are a very professional organisation who, if it wasn't for the obvious reason, I'd say I've always enjoyed working with. If you can find a route in, I doubt you'll regret it - or at-least not often. But, I would regard it as a "next job" after building up credible professional experience elsewhere, rather than something you can aspire to early in your career.
NTSB in the US is a much larger organisation with a very different way of working that lends itself to graduate training schemes (or whatever the Yanks call them), frankly AAIB isn't.
If you are a glider or hang-glider pilot, those organisations (BGA / BHPA) have small teams of (largely unpaid) accident investigators who are partly trained and resourced by AAIB, that might be a route to gain some relevant experience.
G