I think the clue in all this is the quote in the first post, that walk in centres should be run by nurses. However, most walk in centres are attched to doctors surgeries.
It's a walk in centre, therefore there is no need to phone before arriving
If you do phone I suspect the call is dealt with by the doctor's surgery receptionist, who is breifed to say that appointments are needed (i.e. if you phone first the treatment isn't urgent). If you just turned up, i.e. walked in, that option of the receptionist screening the call dissapears. Then you would be assessed by the nurse.