The precise checklist varies from type to type. What you have to remember is that the mil airfield is prepared for the worst-case scenario, ie; we're on a war footing, the a/c is struggling back shot to pieces & the pilot is wounded.
The "cockpit checks" call is a prompt to the pilot. Very often they may already be done. If you're happy with your checks at that point just report "checks complete". If you're doing something at that time just say "wilco" and get back when you're ready.
I have to say when I'm controlling a (small) civvy I tend to tailor what I say. To get it into their language I often use "final approach checks; report complete".
Another possible cause for the confusion with this is that when vectoring the mil don't give the position reports you would get from a civvy unit, ie "turn left heading xxx; downwind" so potentially the pilot hasn't any idea of his position relative to the intercept, and thus no cue for starting the checks.
ap
PS tesco - give your nearest mil base a ring & arrange a visit. They'll be pleased to see you & more so if you're armed with biscuits
Make sure it's a radar unit obviously. If you need a number PM me.
Every little helps!