The Baroness is not wrong about the BBC lack of impartiality. As I've reported previously on MN, some time ago the BBC had an item on their website about Kier Starmer and how he was a PM in waiting. I commented that I liked KS, but while he didn't support the right of women and girls to single sex provision I wouldn't be voting for him. I wasn't rude or sweary.
My comment was deleted as against BBC guidelines.
I appealed. I received an an email that just said 'your comment was against our guidelines'. I appealed again. They ignored me.
To use a good northern term, the BBC are 'shit-kickers' and only report on what they think is important and that isn't the rights of women and girls.
See also the WPath decision.