Difficult to say for sure from the information you've given, but I think I am familiar with the airfields in question.
It is quite likely that the approach controller to which you were handed over was unable to provide a higher level of service than the one offered, either because s/he had significant workload at the time, or because s/he did not have access to the level of equipment required to dispense a higher level of service with any confidence. The destination to which I think you are referring only has primary radar - were you aware of this?
The list of conditions and caveats for the provision of a Traffic Service is quite long and tedious, but the long and short of it is that "pilots remain responsible for collision avoidance, even when flying at a level allocated by ATC". The inference being, as I read it, that if you don't like the level you're at because of traffic or other reasons, it's up to you to change it. Remember that safety is paramount, so if you feel you need to be at 4000ft instead of 5000ft for collision avoidance, advise ATC that this is what you want to do. In extremis, manoeuvre your aircraft as required to avoid a collision, then tell ATC what you've done. After all, you're outside CAS, and you're not receiving a radar control service. The controller is very limited in terms of what vectors s/he can provide under a traffic service - specifically - "a controller may provide headings for the purpose of positioning, sequencing, or as navigational assistance". Note that conflict resolution does not appear in this list, and the heavy inference in our manual is that if a controller does decide to provide vectors for conflict resolution, this should also be accompanied by an upgrade to a deconfliction service (because this, after all, is what the controller is attempting to do). As stated above, it's likely that the controller was reluctant to issue these vectors (and therefore upgrade the service) for any number of reasons.
On leaving CAS, as a London Area controller I will always endeavour to secure you the best possible service from an ATSU outside the limits of my airspace. Now once again, if I guessed your destination right, I would invariably have been offering you to the large military radar unit located just on your right as you leave CAS. They may decline to provide a service, in which case I would seek acceptance directly from the destination ATSU. However, if the former unit declines to provide a service whilst knowing that they have conflicting military traffic in the area (and knowing also that they have better radar kit than the civilian unit down the road), it's my view that they have been fairly negligent in not offering you safer passage through what can be a fairly busy strip of airspace.
Obviously, my view (without knowing more) is based on supposition and conjecture - but my experience says that the unit which deserves the most criticism in this instance is quite likely to be the one you haven't actually spoken to.
LTP