Does the law actually say trans women are women?

No.

This is a relief to me, because really, who gave the law authority to determine ontology? That would just be weird. The law can define categories for the purpose of a law, but it can’t just bang a gavel and say strawberries are luxury automobiles.

Naomi Cunningham at Legal Feminist spelled it out a couple of years ago:

The Gender Recognition Act 2004 does change some people’s legal sex. Obviously the law can’t change anyone’s biological sex. The fact that the law can’t mess with material reality is the point Canute was making when he forbade the tide to come in. But section 9 of the Gender Recognition Act 2004 has the effect that some trans women (i.e. the very small number who hold a GRC – only a few thousand to date) are deemed for most legal purposes to be women, although exceptions apply.

Mind you, seeing how it’s been playing out, I think that’s too much too. I think the Gender Recognition Act was a mistake. At any rate the point is the law doesn’t magically change the ontology.