Well, that’s opened up even more questions! 
Hadn’t thought of SSIS. Loch Doon is, it turns out, a SSSI… because of a rare type of fish that breeds there, not the Osprey.
But…
Seems the legality depends on the particular requirements of the individual SSSI, which are here:
Only bit of that that might apply to drones is the SOAC… which itself is murky:
Haven’t posted the letter yet (because, of course, Police Scotland don’t do emails from Joe Public), so might have another crack at it to ask if they’re using the SSSI and, if they are, whether that’s an official Police Scotland stance on the SOAC.
