The holder of a PPL with a Single Engine Piston (Land) CLASS RATING can fly any aircraft with a single piston engine designed to operate from land (as opposed to one which operates from the sea / water).
If an aircraft has 'complexities' (like a c/s prop, retractable gear, tail wheel etc) then you would need differences training from an instructor in respect of each complexity.
There are a few exceptions to this however. LASORS lists a few aircraft (the piston engined Piper Malibu springs to mind) which would seem to appear to belong in the SEP (land) class but which the CAA has decided are sufficiently complicated as to require a type rating.