Assuming you wish to continue flying a PA-28 (which is an 'EASA aeroplane') after Apr 2020:
1. Complete refresher flight training as required.
2. Pass an SEP Class Rating Proficiency Check.
3. Obtain a Class 2 Medical Certificate.
3. Apply to the CAA for issue of a Part-FCL PPL with SEP Class Rating.
Other options are currently available, such as a 'Pilot Medical Declaration' - but the long term future of that cannot be assured. By the time you get your licence, the PPL will also include LAPL privileges, so you will be able to let a Class 2 medical drop to LAPL medical level and fly under LAPL restrictions (2000 kg MTOM, no more than 4 PoB, VFR only).
The old brown PPL will not be valid for flying PA-28s after Apr 2020; even if you had it re-issued, it would only be valid for flying non-EASA aircraft (e.g. Chipmunk, Tiger Moth) after that date.
As far as written exams are concerned, the only one you might have to resit is the Communications (PPL) exam if your FRTOL had an expiry date - but your training organisation should be able to advise further.
Last edited by BEagle; 3rd Jul 2019 at 15:15.