I work in a GP surgery and this is definitely the sort of thing your GP would be happy to see you about! It doesn’t have to be clinically urgent at all to see a GP, and they might be able to help your symptoms in primary care anyway without an onward referral. All it means is that you won’t meet the criteria for an urgent GP appointment (same day, usually for chest pain/respiratory issues/lumps etc), but you can still get an appointment within 1-2 weeks, if not quicker depending on your area/doctor. If they can’t help, then yes the NHS referral to dermatology will come from your GP, who’ll send it to your closest hospital unless you request otherwise. Waiting times vary depending on the hospital, but please note that in my area the routine waiting time for a dermatology appointment is about 9 months…. It will be free apart from some small costs for prescriptions if relevant. To avoid this waiting time, your GP may just ask for advice from the dermatology consultants on appropriate treatment instead, if suitable.