It's all fearsomely complicated...by not converting it already I've made my life harder I think. I'm sat here wondering whether I should just go to France for a week, eat cheese, fly aeroplanes, get the EASA.
(If someone could speak to my wife about this idea, it would be much appreciated).
After a lot of probably unnecessary searching I found "third-country-licence-conversion-requirements-from-1-january-2023" on the CAA site. (Sorry, URLs not allowed yet for me.)
It seems to me that I fall under Route 3 there as an “EASA PPL(A) that previously held a PPL license with the UK CAA”.
This means I would need a proficiency check (which I expected) but that's kind of it.