For the US Army we did 8 weeks of intense basic training with the drill sergeants yelling at you and all that shit, you get in crazy good shape during those 8 weeks. Then after we do this thing called AIT which is where you learn your job, it lasts depending on what you pick for a job. If you're Infantry they just tack on 4 more weeks of basic training basically. If you go to a technical field it could be up to a year of training learning your job.
They don't usually turn down overweight people, cause they get you in shape, if you're insanely overweight though they'll tell you to come back when you get in better shape.
No idea how it works in the UK though, you could probably check out a recruitment website.