I got a response from the BBC. In their view Evan Davies was entitled to call Miller "anti-trans" all the way through the interview even though this phrase did not reflect the contents of the High Court judgement because Davies didn't call Miller "transphobic". The official view of the BBC of the debate is that one side is "pro-trans" and the opposite side is "anti-trans". How limited and binary is that?
The BBC ignored other parts of my complaint.
That's another step down in the level of respect I have for the BBC. By the time I'm done I'm going to be over on the side of cheering the abolition of the TV licence.