As others have mentioned, you need to go see your GP and he will refer you if he thinks you need to see a specialist.
Waiting lists obviously depend on where abouts you are...London - it's hard to say really since there are a lot of people in London, but probably many dermatologists too! From my experience, it can take anything between a few months and a year! I needed to see a dermatologist in Wales and had to wait for over a year. In the end, I went to uni so asked to see a dermatologist there instead. This took about 3 to 4 months if i remember correctly..
So yeah, just go see your GP.