OP, you seem to think that this is all about toilets. I guess I understand why so many people focus on that, it's probably the first thing that comes to mind when you hear the phrase 'women-only spaces'. Maybe it's the only women-only space you've ever been in.
But we're actually talking about domestic violence shelters, prisons, hospital wards, psychiatric wards; even sports. Oh, and scholarships in STEM subjects because it's recognised that gender socialisation dissuades girls from studying them.
Ask yourself why these women-only spaces exist. Why they have ever existed. Could it be to ensure the safety of women? Or their dignity? Both these things are pretty important.
But you're focussed on toilets, so lets talk about toilets.
"Do you really think a man is just going to stick on a wig and a dress and pretend to be trans so he can assault women in the toilets?"
It would seem that you think this is inconceivable. Why is that? What makes you think the type of man who will spend months, years, grooming victims, wouldn't be willing to make so little effort? Not that he has to make that effort anyway - just has to say he feels he is really a woman. If you don't believe that, the photo I've attached is on Danielle Muscato and her words of wisdom. Admittedly not in the UK. For UK, google Alex Drummond, who wants to widen the bandwith of gender.
So, given that some transwomen don't feel the need to present as women, that gives men who are not transwomen an 'in'. They just have to say they're trans. No effort required. Probably quite appealing to , say, a teenager wanting to show how big he is and how uncomfortable he can make women, and all without having to do anything that could lead to charges. Sweet!
Perhaps you haven't appreciated the difference between normal people and predators. They don't have to assault you to get their jollies. They can savour your discomfort, your realisation that you can't do anything about their behaviour, your helplessness, your inability to take any action against them. It's a win-win for them.
Now, you mentioned your "friend who is a transwoman and she is the kindest most gentle soul you could ever meet ". She will not be immune in this scenario. Indeed, a predator may find it extra-exciting to discomfort a transwoman.
So please, get off your virtue-signalling high horse and think about what's happening. The world is changing, we need to accept that and have our laws, our institutions, our social conventions in place to accommodate those changes. But we need them to be thought through so that they offer everyone - women, transwomen, transmen, men - safety and dignity in their lives.