The unusual thing about this clinic is what the booking form actually reserves. It is not a place in a queue and it is not a dentist. It is a chair.
Four chairs: one and two in the front room, three in the quiet room at the back, and four, which belongs to the hygienist. When you book, one of them is held with your name on it for the length of the appointment, and the confirmation email says which.
It is a better fit for how a dental clinic really works. Two dentists share three chairs across a session, because a filling that is setting does not need a dentist standing over it, and the chair is the thing there is never enough of. Booking the chair means the diary cannot promise a time that no room exists for, which is what happened here for two years.