The requirement is to obey your licence privileges.
For a non-IMC-rated pilot this means flying VFR (min vis 5 km) or SVFR (min vis 10 km unless notified lower) in controlled (A to E) airspace, and flying with a visibility of at least 3 km in uncontrolled (F/G) airspace. There is no requirement to maintain VFR in F/G, but if you don't, instrument flight rules on minimum altitude ("1000 ft rule") and cruising levels ("quadrantal rule") apply.
For an IMC-rated pilot, it means flying VFR or SVFR (min vis 3 km) in class A/B/C airspace. In D/E/F/G you can fly IFR too. This again requires compliance with IFR, which in D/E now includes the requirement for an ATC clearance. The only limitation, VFR or IFR, is a minimum flight visibility of 1800 m for take-off and landing.
homeguard, I think you are mistaken in saying "A JAA PPL is allowed to fly at the VMC in-flight minima" if by "JAA PPL" you mean one issued by the UK CAA. Schedule 8 Section 2 2(b) repeats the restrictions imposed on a UK PPL holder of 3000 m minimum flight visibility etc. That probably resolves the contradiction, doesn't it?