The first time I went to the doctor about depression, I got an emergency appointment. In my surgery, you book on the day, and by the time I rung, all the slots had gone, so they got a doctor to ring me, who then managed to get me an appointment for that day.
I'd definitely recommend going to the GP about your depression - for me, it's really helped having support from my GP. For me, when I first went (to my current GP, I'd been once before at home), she recommended a combination of therapy and antidepressants straight away, as it was quite severe and it had been going on a long time, although I declined ADs for a few months. It's likely that they'll ask you to fill in a questionnaire and discuss your symptoms with you, and then decide what the best course of action would be.