It was the Labour party bureaucracy, who are overwhelmingly dominated by the right of the party doing everything they can (fair or foul) to prevent the "far left" from having power (see reports now circulating re the Forde report into exactly this). The process was then sent into overdrive when Starmer became leader and decided to use it as a brazen tool of factional warfare against the left.
As for your second question, I'm going to depart from the consensus of the thread here and say I don't see how the favouring of trans rights over women's rights (much as I oppose it) is particularly "authoritarian". People from the TWAW side of the fence would probably say exactly the same thing about the opposite.
Authoritarianism is defined by how happy you are to have a particular way of doing things forced on people, rather than arrived at by agreement; how happy you are to push through simple solutions based on exercise of power by one group over others rather than more nuanced ones based on negotiation and the sharing of power.
I don't see any evidence that Billy Bragg is particularly authoritarian in this respect. I disagree with him because I think he's wrong. But he's entitled to his opinion, and the way he lives his life and expresses his beliefs doesn't seem any more authoritarian than the way I do.
There's always power being exercised somewhere. I think the problem here is that what people call "authoritarianism" is often just the exercise of power they're unfamiliar with, by people they don't like doing things they don't agree with. Whereas a similar exercise of power by people they like doing things they agree with doesn't seem authoritarian at all.