Under simple CAA-only rules i.e. UK airspace, a G-reg plane and a UK issued PPL, the pilot can fly IFR (which includes filing a flight plan to that effect, either an airborne one or the full ICAO job) provided he remains within his VFR rules (3000m vis, clear of cloud, in sight of the surface etc) and remains in Class G (or, not exactly applicable to the UK, E or F).
What would be the point of a plain PPL flying under IFR?
IFR traffic gets a better service from ATC, and is much more likely to get a radar service, so that could be one reason. But this won't cut much ice if there is wall to wall sunshine everywhere; ATC do have windows too
I suppose that an experienced PPL flying in marginal VFR conditions would be better off calling himself "IFR".
As for putting "IFR" on an ICAO flight plan, that is something I don't see any point in. Especially if flying over 2000kg