Sun Who, yes, the LOS issue is nothing like such a problem.
We concentrated on generic issues - if they could be solved for drones half a world away, they would work in LOS conditions.
I don't know what the climb performance of long range drones is, but a simplistic view would be to base such drones as far as possible from busy airspace and centres of population. Ascension Island, perhaps? Excellent connectivity with geostationary satellites, of course.
I simply don't see the UK genpub accepting military drones flying from somewhere like Waddington during daytime. If the military mind is so keen on drones, then it'll simply have to accept the consequences.