Doctors are going to communicate with each other about their patients if they have concerns. It not gossiping. Yet it's not nice when they seem to back each other up. I am sorry you feel betrayed.

Doctor A did not let you down.

You seems to have been given a full explanation of what conversations have gone on. Why does Dr C get to make the decision? Is he the boss where Dr A works? I don't live in the UK so I don't know what your options would be. I trust that some-one who does live in the UK can help you with some form of resolution.