My understanding is that to receive remuneration as a pilot (ie ‘a salaried single pilot’) then you require at least a CPL(H). A CPL requires a Class 1 medical. This includes NCO/NCC flying, as well as CAT.
A loophole seems to exist where someone is employed as, say, an Estate Manager or Gardener but with ‘additional duties’. (ie chauffeuring or flying). This could be done on a PPL. However, I’m not sure of the legality of that situation (or if it has ever been tested in the law courts).