Yes - at yours! Where you went somewhere miles from a+e, not in the room next door so obviously basically part of the whole a+e system as per steppemum (which is why she thinks we are terrible for suggesting going to a+e, at hers you get sent next door. I still don't think that's a big deal. Would you have found that a big deal?)
You went somewhere with daytime only opening hours and chose to sit under a poster for four hours telling you that 111 calls were prioritised (and didn't at that point call 111 to get said appointment or to check if you were in the right place) and then chose to go home instead of to 24 hour a+e.
Steppemum's situation is actually far worse. Apparently there broken bones are not dealt with at all by a+e so it's a daytime only service and you get turned away from a+e when it is closed. I say apparently as I would be very shocked but it could be true, things seem terrible these days.
Your wait for triage was appalling but why the rest of it? That part is on you. At least a 4 hour wait somewhere that is open 24 hours makes some kind of sense. That's assuming your urgent care can deal with fractures that turn up rather than referred via a+e/gp. Mine can't but if yours can, great. You'd hope they would tell you as you book in, as per steppemum in reverse. But possibly only after triage, which would be poor!
Steppemum's situation is actually far far worse. I worry for us all if fractures are considered a daytime only non 'accident or emergency'.
Anyway I am glad you got things sorted. The wait is disgraceful. I've learned to always phone 111 for advice from this thread. I did actually remember doing that a few years ago for something and being sent miles away to what was probably an urgent care centre I didn't even know existed til I phoned! That was an appointment system as well. Left to myself I would have gone to a+e but it worked out probably quicker. So 111 seems a good call.