I love these propaganda movies - eg Millions Like Us, which does much the same for a bunch of girls making aeroplane parts in a factory. (Is there a government unit filming heroic lorry drivers as I type?)
A disparate group of men are called up: barrack-room lawyer Bernard Miles, fish out of water Raymond Huntley (such a good actor), mother's boy Peter Ustinov, token Scot John Laurie... The weed among them turns out to be worrying about his children, there's a heartless corporal trying to lick them into shape, they spend a lot of time cleaning their boots. Huntley, the desk wallah, types many letters to the Ministry of Labour complaining about their "mistake", but eventually finds a berth in Signals.
It was remade as The Way Ahead, which I remember as less gung-ho, and then, surely, again as Carry On Sergeant?