How exactly do you see a Doctor in the UK?

Been registered with this GP for about a year, I cannot change as this is my catchment(?) area. All roads lead to the phone service. If you walk up to reception? Referred to the phone service. eConsult? Clicking this causes a telephone number to appear and nothing else.

If you phone the number, it either says "we're too busy" and hangs up, or I am placed into position 10 in the queue, only for the voice to say an hour later "we cannot complete your call, goodbye". It doesn't matter the time of day or the day itself. 111 seems to be closed during the times I can call and refers to 999.

This isn't an emergency so I'd rather not waste 999 or the emergency rooms time. How exactly do you get medical help?