VFR
I0540 makes the points with regard to why some aircraft are restricted to VMC. I'm unaware that any are restricted to VFR only.
Controlled airspace VFR's apply higher minima VMC such as 10k visibilty instead of 1500m. Surely where the aircraft is restricted to VMC minima (1500m) and to the vertical and horizontal distance from cloud (that varies with +/- 3000 altitude within the UK) that is the restriction and individual controlled airspace minima is not relevant with regard to the aircraft Cof A.
Within the UK flight at night must be conducted in accordance with IFR but in VFR conditions unless the pilot holds an appropiate rating to fly within IMC (a condition which is simply when the VMC minima is not met).
Outside of controlled airspace there is no restriction with regard to navigation equipment to be carried. VFR/IFR are simply a set of rules that the pilot chooses unless within IMC when IFR is obviously mandatory and I know of no other prescribed requirement for equipment. An AOC will have its own set of mandatory rules and operational requirements.