In reference to NPAS's 20/30 minute circles, looking at the map on ranty's link, I think it shows that the UK has in fact some pretty good air cover.
In the south and the Midlands, coverage per sq mile yes. Definitely not in Scotland. Wales ? Northumberland?
Les french piloteurs are fully qualified policemen, actually the commander of an aircraft has some special rights regarding law enforcement as far as I remember.
To some stage they can somehow act on behalf of the state attorney.
C'est la vie - en France