There is no perfect system and sadly, some rare cases will be victims of it. You could argue that without 111, there would be thousand of extra cases showing up at A&E, which would put a lot of pressure on it, creating even longer times, stress on the staff, and that too would result in misdiagnosis and people dying as a result.
I do tend to agree though about the reliance on strangers rather than our own. Sadly, some people will think that with a fever of 38.5 and a cough, they are dying and need urgent care, whilst others will believe that with a fever of 42 and spitting blood is not an emergency and worthy of just waiting at home to see it better. It's the former that put pressure on the system, but no matter how you tell these people that they don't need urgent care, they will not listen.