As you are VFR an ATCO cannot technically require you to fly at a specific altitude/track as you may need to change either to remain VMC. Notwithstanding this, to expedite a CTR or CTA crossing it is a common practice to do it in the UK, I did it frequently, however with the proviso "advise if you require to change track or level to maintain VMC".
With respect to "radar control service" UK MATS Part 1 (CAP 493) requires ATCOs to change their service from an ATSOCAS when entering controlled airspace, in this Class D. However this opens a proverbial can of worms as to what is technically correct.
As you are VFR you cannot in the UK technically become a controlled flight as this could be seen as "controlled VFR" which is something that the UK does not practise, and would require Class C airspace to do it in. Class C control zones and lower airspace contol areas are not available in the UK.
My advice would be tell ATC if you expect/require to change track or level to remain VMC and put "radar control service" down to something that UK ATCOs have to say to avoid getting their knuckles wrapped by their unit examiners or the CAA.