scifi: It's the controllers' responsibility to advise you of relevant traffic, notwithstanding 'frequency separation'; that's what he's there for. Even under Basic Service:
2.3.1 Basic Service provides advice and information useful for the safe and efficient conduct of flights. This may include weather information, changes of serviceability of facilities, conditions at aerodromes, general airspace activity information, and any other information likely to affect safety. The avoidance of other traffic is solely the pilot's responsibility.
2.3.3 Pilots should not expect any form of traffic information from a controller/FISO and the pilot remains responsible for collision avoidance at all times. However, where a controller/FISO has information that indicates that there is aerial activity in a particular location that may affect a flight, they should provide traffic information in general terms to assist with the pilot's situational awareness. This will not normally be updated by the controller/FISO unless the situation has changed markedly, or the pilot requests an update. (My bold)
Notwithstanding the very clear definition above (my italics) as to to who is responsible for what, the controllers' wretched 'duty of care' caveat also plays a part and leads to accusations of controllers 'over-controlling' in Class G airspace. You're damned if you do and very damned if you don't.
Mil controllers have an unenviable task of providing IFR ATC services to high workload aircraft (frequently single-crewed) in completely unregulated airspace where their high performance requires the use of a high airspace volume; providing 5NM and 3000ft separation under Deconfliction Service against unknown traffic in the Vale of York/Lincolnshire AIAA is no easy matter.
So don't be 'that guy' snurgling along, 'VFR' at 800ft, clear of cloud and in sight etc, under - but across - a MATZ panhandle "because I can" - just call; there's no charge!