Lets play with some numbers here.
There are no reliable figures for the UK Trans population. Stonewall says that their 'best estimate' is that 600,000 UK people (1%) are Trans or Non-Binary to some degree.
Let's suppose that all of them are transitioned/transitioning (they aren't but whatever) and let's ignore "non-binary" for this exercise.
So that would mean there are a maximum of 300,000 "Assigned-Male-At-Birth" people in the UK, and let's say they all want access to women's single-sex spaces.
A certain percentage of the UK population are scary dangerous people. Let's say for argument's sake that that figure is 1%. (I have no idea). That's also 600,000 people.
Lets say that men are 10x more likely to be scary dangerous people than women. (I tried to google some stats for this but trust me, you don't want to go there. It's nothing like 10:1 whatever way you skin it)
So these figures (that I admit I've pulled out of my digestive system) would state that:
5,400 UK Trans women are scary and dangerous
60,000 UK Women are scary and dangerous.
So, based on my shitty numbers, you are about 11 times more likely to meet a scary dangerous woman-woman than a scary dangerous trans-woman.
Anyone care to reality-check these figures?