I had a horrible mole on my face (a Nanny MacPhee one!)
I was referred to the hospital dermatology dept, and they told me it was purely cosmetic, and therefore it couldn't be done on the nhs.
I decided to find out about having it removed privately, and saw a doctor who said she found it quite reasonable that I didn't want to end up with a mole which was taking over my face, and she felt it should be done on the nhs. She wrote to my doctor and asked him to refer me straight to hospital to get it done, without having to go through the dermatology dept again.
It was done, and I'm no longer frightening small children (well, not often!)
So, I think there is an element of pot luck. My GP was quite cross: he couldn't understand why I would want it removed when it was benign.