Gaza: "You cannot fly G Reg aircraft on an FAA PPL. "
(The sounds of cash registers echoes somewhere in the distant past... .

) sounds like the voice of the CAA circa 1991 - ask the question 'can I fly in the UK on an FAA PPL?' and get the answer tp a totally different question namely 'how do I convert a FAA PPL to a UK one'. Doesn't happen nowadays, I quickly add!
Of course you can fly G reg - day vfr, uk airspace, plenty of punters do it, just keep your FAA ticket fully valid. Personally having checked out 'both' FAA and SA new PPLs and I reckon SA courses are more suited to UK environment, but we welcome FAA or SA licence holder at our airfield.
I have rented and undergone training at one SA school (Algoa), and liked what I saw.