I seem to recall a few years ago the story of a civilian who arrived at a well known Mushroom farm base, and announced his arrival by driving his car into a building on the camp, totally ar$eholled.
The RAF police said that they couldn't breatherlise him as he was a civvie and they had no powers over him, so they called in the Civvie police.
They said that they couldn't breatherlise him, as the incident occurred on MOD property and they had no powers, and thus the chap was eventually let off, with neither bunch of policemen knowing who could do what, and to whome. A complete shambles.
Makes you wonder why we have civvie policemen at military airshows I suppose.