The way it worked when I last paid a visit to NHS Scotland was you got a choice when you walked in the door.
For Doctor go and sit over there and wait.
And if you will accept a (something) nurse go through there.
I went for the nurse option due to reckoning if it needed a Doctor you were always in the system anyway. And a Doc did come through for a quick look anyway. Tetanus booster which I volunteered to let a trainee doctor do which doubled the time to be treated but was a laugh and a half. And out the door.
More than happy with both my care and speed of delivery. And if I ever go back again I will definitely be going for the nurse option again.