Thanks for the detailed info ORAC, I'm probably making the mistake of comparing things with the excellent service we used to get from RAF (and other NW European) military radars way back in the 70s. In those sort of circumstances, I would have expected Northern Radar, say, to contact the appropriate civilian ATC authority to ask, for example, if they knew anything about an unidentified contact approaching the coast.
Mind you I do recall the occasion when they asked us to look out for "friendly traffic" on a reciprocal heading, just as two Badgers flashed past on our starboard side. But then, nobody's perfect.