So there was a question earlier today in one of my groups about TERFs in the UK, why are they so strong there, etc. Let me elaborate on something.
There is something special in mainstream British feminism that is quite different from European feminism(s), but since the English speaking internet concerns mostly the Anglosphere and not Europe, due to us having separate, isolated debates in each country/language, you won't likely ever hear how the UK is substantially different.
It is important to understand the logic of British feminism. Unlike European feminism, which is mostly inclusive and focused on stuff like equal pay, care, safe design of public space and general equity, in the UK it was always about "separate but equal".
British centres of power were always men-only, and many British feminists didn't react the way European women did (aka pushed their way into male spaces, so that these became co-ed spaces), but created their own, separate spaces, which they then aggressively policed the same way British men did with theirs. Add some Victorian prudishness and bioessentialism, that was abandoned in Europe after WWII for obvious reasons, but not in the UK, and voilà , here come British second-wave radfems and the TERFs.
I am from the Czech Republic where I currently live; I lived in Norway, Poland and the Netherlands, I speak fluently multiple European languages and understand few others; I don't say that to brag, but to show my ability to do the comparative analysis, since I study the topic closely.
Out of EU member states, only in Bulgaria and Hungary are trans rights worse than in the UK at the moment, with Hungary being expected to get substantially better soon, and in neither of those two countries are trans people, and especially trans women, as demonised as in the UK.
In all EU member states transphobia comes exclusively from far right places; it is unheard of that liberals or anyone non-far right would say what is absolutely the mainstream in the UK, including Hungary and Bulgaria.
If you are saying the stuff JKR is saying, you are 100 % aligned with far right politics.
We had an attempt by a group of our far right senators to enact a bill proposal similar to what is in the UK, but the proposal was killed within a week before it could have been even voted upon in the Chamber of Deputies. Just for instance.
Scandinavian feminism is focused mostly on fair share of care and chores, German feminism focuses mostly on equal pay, Kita for everyone and the like, Polish feminism is mostly about access to abortion, Czech feminism is mostly about equal pay and safety from domestic violence - I could go on, but all in all, men are welcome to participate and the goal is to create equity for everyone, regardless of their gender. Together.
We don't get British obsession with separate spaces for women, women here are absolutely fine with the way things are, mostly because cultures in the Continent are far less prudish and overall we treat men and women as one people rather than different species.
Moreover, because of civil law rather than common law, we have different approach to legal texts and their interpretations; this makes it different too.
Not just regarding trans rights, but also regarding women's rights, I am often amazed by how much backward the UK is in so many ways compared to the EU (again, including places like Hungary, this needs to be stressed). I often see women in English-speaking debates saying things like "ugh, men" on things that actually concern problems that are specifically British and that stem mostly from both societies' tendency to separate already boys from girls, treating them differently and sexualising women in contexts we don't really see as sexual at all.
We can't really get this across the Channel, because we just don't have the power to do so. For instance Czech debate on feminism is quite isolated; it's interesting, but no more than 15 million people would ever be able to participate in it (CZ/SK) due to the language barrier, the same goes for Scandinavia (17 million), Benelux (28 million), Poland (38 million), or even DACH (95 million). It is nothing compared to half a billion people of the US, UK, CA, AU, NZ and IE that are giving tone to the worldwide debate in English.
So, if you are a British trans woman, you would do yourself a great favour if you moved to mainland Europe. You will be welcomed and cherished (for the most part).