However, you will need to validate and ultimately to convert any 3rd country PPL if you wish to fly EASA aircraft after 2019 at the latest in some EASA Member States who have applied the Art 12(4) derogation.
Pilot who only hold FAA PPLs and who are resident in the UK must now meet the requirements of ORS4 No.1220 if they wish to fly EASA aircraft (e.g. Cessna 152/172, PA-28) in the UK.
EASA aircraft does not mean 'EASA registered'.
Also, any EASA training will only be possible at an ATO or DTO after next April - RFs will no longer be permitted - and a DTO cannot be established outside an EASA Member State. Quite how many non-European ATOs will bother with the EASA PPL after Apr 2018 is frankly open to doubt.