//NJ, they are not allowed to turn anyone away from A&E. They can only triage you last.//
In my local A&E, pixie, (the one I took the guidance from) if you are triaged as not dying (or similar) you are not permitted to wait. You are told to ring 111 and they make an appointment for you if their "triage" system determines that you need it. Whether they are "allowed" to turn you away or not makes no difference because that's what they do. I have spoken to two people who have endured exactly that. Both returned to their cars and made calls to 111. One had an appointment made for him for an hour later; the other did not. She was told by 111 to consult her (that is my) GP (who had refused to see her and told her earlier that day to attend A&E). She returned home and became so ill two days later that she had to be collected by ambulance. I know this because I called the ambulance for her. These are not fantasies, they are things that have happened to my acquaintances.