@sunshinechaser if you are worried at any point, and can't get anywhere with your GP, and you want him to see a dermatologist, then you can self refer to a consultant these days for private treatment. Face to face is around £250-£300, online via video is generally under £200. For this practice, for example, it's £185.
https://skinassist.uk/dermatologist-near-me/acne-booking-page/
When I was fobbed off by my GP about concerns re a skin issue I self referred to a consultant at a local Nuffield hospital, mainly because the consultant who did one morning a week there was a cancer specialist, and at my age that's always the concern, especially as a family member died of melanoma.
I got a swift diagnosis (not what the GP thought it was, but fortunately not cancer) and given options on treatment. I also got a full skin check, including my back for any potentially sinister moles etc.
All the logjams in the system where I live seem to be at the GP end, it takes 3 weeks to get an appointment, if you can convince them you need one after filling in their forms.
A generic google search of "consultant dermatologist UK" will bring up lots of options, that's the route I took and then looked at Nuffield because there is one within easy travel distance for me.