Well, I don't accept your premise, for a start, but I see where you're coming from, and okay, it's as neat a way of laying out the dividing line between two interest groups as any.
And secondly, I don't accept that "patriarchy" has done anything of the sort. I realise, of course, that the bulk of the legislature and judiciary is male, and generally represents the patriarchy. It does not, however, follow that every law passed represents a position held or declared by the patriarchy. When feminist lobby groups get laws passed or amended in ways that support women, that's not a case of "the patriarchy declares that, e.g., you can be raped by your husband".
I also don't accept that women weren't consulted. But I'm a bit lost as to how to refute that since, I'm fairly sure, if I point you to the Parliamentary debates and the breakdown of votes and the fact that the Chair of the Parliamentary Committee on Transgender issues at the time the legislation was passed was a (cis, as far as I know) woman, the argument will be that men get women to do their dirty work.
The Gender Recognition Act is hugely threatening to the patriarchy, IMO. I know we're talking about trans women here, when we're talking about semantics, but don't forget that law also gives the same rights to trans men. So if you're talking about privilege, doesn't that law potentially open the patriarchy to having people without penises demand the privilege and access that they enjoy? For every trans woman who is appointed to a female-only job, there's the spectre of a trans man demanding access to male-only clubs, higher pay and the right not to be harassed on the street despite not having a penis. Can you imagine the patriarchal horror?
I keep coming back to trans men because, if the bill only recognised trans women, I'd have more sympathy with your argument. But it recognises both, and so your arguments have to apply to both. Pogleswood is saying the same thing.
Certainly in Australia, legal recognition doesn't just smooth the way. A case here a couple of years ago rejected the application of two trans men who had both undergone double masectomies, were taking testerone which rendered them infertile, but hadn't had hysterectomies (under advice from doctors saying it was too risky an operation). The Board has discretion on an individual basis. I think that's the case in England too. I'm mentioning that because it seems clear to me that in effect the patriarchy is still fighting back pretty hard against trans recognition.