I have not done a lot of investigation, any comrade with better knowledge is welcome to correct me.
It's my understanding the problem is the different waves of feminism. Second wave feminism took hold in the UK and informed a lot of the rhetoric and social understanding of gender, they tended to be more focused on biologic sex markers and tend toward anti-trans positions. UK women's groups and feminist organizations still tend toward this second wave. Whereas in the US It was third or fourth wave feminists that really took hold on campuses and was the base of a lot of the political groups.
Shaun has a video on transphobia in the UK that might be enlightening. https://www.youtube.com/watch?v=91_5OOmK1TQ