You can fly a UK G-reg on an FAA PPL without validation or conversion. That regulation might get shut in the future, but as for now it's legal (as far as I know). What you can't do is go abroad with a G-reg and your FAA license (a few countries accept it), but as long as you stay in the UK you should be fine. You can always go abroad with a N-reg, of course. And there's plenty of those around.