OK, tricky question without knowing all of the circumstances. It's not a call that I would make myself nor is it a standard phrase in the UK civil world - and I'm not sure what might make it necessary. I would try to give more specific instructions to each aircraft if time permits - if there is an aircraft inbound with an emergency (the only circumstances that I can think of where one might want everything to land in a hurry), subject to a couple of provisos I probably would try to persuade aircraft to stay airborne.
To respond to your specific examples, joining on an extended downwind (i.e. clearance has been issued) I would consider to be in the circuit. The phrase 'approaching initials' suggests this is a military field - so I am not the best person to answer, never having thought I look good in a uniform. The mil procedures may give a definitive answer but my own view is that, no, that's not in the circuit yet. On the climb out....if the aircraft is departing (even to the local training area) no, not in the circuit but if it planned to do circuits, then yes.
But this is all a bit subjective - feed me a bit more info and maybe I'll refine my answer (=change my mind).