These are the closest to the Algarve, so you might ask them :
AERONAUTICAL ACADEMY OF EUROPE - Academia Aeronáutica de Évora, S.A.
Still, a bit far...
Other than that, besides the previously mentioned Gestair there´s Leávia, Omni, and the Aero Clube de Portugal flight school, all at the Tires (Cascais) Airport.
I don´t know of a school in the Algarve doing PPLs, but that doesn´t mean there isn´t one.
Good luck.