Legislation like this seems performative (and could possibly stem from actual transphobia rather than the not-actually-transphobia-at-all kind), and in the UK I can't at all see why it would be helpful.
Now that it has been clarified that it is legal to have single-sex toilets (and that it may be discriminatory against women not to), I think we are fine with the status quo that persisted until trans activism sought to disrupt it.
That status quo is supported by two things:
Firstly, now that toilet providers can be confident that they are acting legally from the point of view of equality law, they can take action where needed. As I understand it, if you break the Ts&Cs associated with your right to (e.g.) enter a shop, use a gym, etc. you can, under civil law, be required to leave the premises, and, where applicable, have your membership terminated.
And second, now that the law is clear, I'm guessing that the kind of activism that encouraged men to violate single-sex toilets will begin to die down, and we will return to the only real plausible and sustainable means for enforcing single-sex toilets - namely, public understanding and a general acceptance of a need to follow the rules.
Any claim that more draconian enforcement is needed just plays into the TRA narrative that single-sex spaces are somehow terribly difficult, complex and unusual things.