yaffle,
The original question was do aircraft operating in Class D and E airspace HAVE to be under Radar Control. The answer is no, irrespective or whether they are operating IFR or VFR.
MATS PT 1 clearly states that Approach and Area Control units shall provide their respective types of Control Service with or without the use of radar. No where does it say that IFR flights must be under a Radar Control Service.
What happens when Transfer of Control takes place to the Aerodrome controller, he/she by definition can not provide a Radar Service? What about when the radar is off for routine maintainance and there is no back up?
With respect to VFR flights, they can be placed under Radar Control and not just be receiving an Approach Control Service. My unit will quite often vector VFR traffic for an instrument approach under VFR when requested.