Well, I'll shove my usual tuppence worth in here which stirred up all sorts of negativity last time I said it.
I have NEVER been given a Radar Control Service when entering Class D airspace VFR. Our local ATC unit NEVER tells VFR transits they are under a Radar Control Service.
This is all perfectly fine and in accordance with MATS Part 1 Section 3 Chapter 1, which states that the service to be provided by Approach Control within Class A to E airspace is "Air Traffic Control Service
with or without surveillance". In this case they're giving Air Traffic Control Service without surveillance. In almost all cases this is for traffic which has been under a BS before entering CAS, so not providing a radar service is entirely consistent with the previous service provision.
Just because you have a radar it doesn't mean you have to provide a radar service, whether your traffic's inside CAS or not.
NS