Op the original theory was that a small group of transsexuals (about 5000), who were mostly effeminate gay men with gender dysphoria could legally change their sex and it not be challenged. It was assumed they'd 'pass' sufficiently to make it a matter of personal privacy. There was one particular man who said if he changes jobs, he wants to go to the next job as a woman and not have anyone know the truth.
The criteria was 'living as a woman' for 2 years (which now means supplying some documents with a name change) and having a diagnosis of gender dysphoria. Surgery wasn't necessary. (And nowadays you can get a diagnosis of gender dysphoria very easily).
It was assumed that only a handful of men would take it up. And actually only about 6000 gender recognition certificates have been issued, so they weren't far off.
Then stonewall changed the word to transgender and included part time cross dressers (a fetish), drag queens, and basically any Tom Dick or Harry who says they're a woman, with absolutely no need to change their clothing or alter their appearance in any way.
Then a whole bunch of lobby groups got it taught in schools as akin to homosexuality, and therefore a civil rights issue.
And before you know it, children think they're born in the wrong body if they like the wrong toys, and anyone is a woman who says they are, including cross dressers and drag queens.
Of course, this wouldn't fly quite so quickly if it hadn't been backed up with the mantra 'no debate', underpinned by threats of rape, violence and loss of livelihood if anyone even slightly disagreed.
And yes, the conflation of sex with gender that you have noticed, is entirely deliberate.
Make no mistake. This is a political movement, and was started decades ago. With tweaks to laws, long-term infiltration, and the deliberate ploy of aligning it with LGB.
As a last minute failsafe, parliament did say that there would be certain exceptions where single sex spaces should be the norm. And they actually mention sport, refuges and any women only spaces where women want them to remain single sex. But they didn't make it enforceable. They made it optional and up to the discretion of the service provider. Making the assumption that no one in their right mind would eg send rapists to women's prisons.
And that's the problem. Every service provider in the country has been successfully lobbied. And trans ideology is taught in schools and universities.
The law is absolutely in place to stop this nonsense, but people are too frightened to implement it.
As mentioned, Helen Joyce's book 'Trans' will reveal everything.
And, if there was the slightest possibility of her being sued for defamation of any kind, she would've have been. You can take from that that her book is entirely accurate.