Step Turn,
The answer is, it depends on when & where you want to fly. The current EASA rules are very simple, you need an EASA licence to fly an EASA aircraft in EASA airspace.
However, we are still in a transitional phase where EASA rules are not yet compulsory, individual countries may choose to apply their old rules until April 8th 2016 (although that date may change again.) The UK is one country that still applies the old rules so your ICAO PPL is legal for VFR non-commercial here, other countries rules will be different. The only certainty I can offer is that getting yourself an EASA PPL will cover you through EASA-land.