My understanding is that yes, of course an organisation can decide to include TW, but if they do so: the space becomes mixed sex by definition, and so other men can’t be excluded on the basis of their sex.
I do think they would be free to convert a women’s space into a mixed sec space in many circumstances (not schools or employers, as these are covered by additional legislation requiring single-sex facilities), but if they do that, they would likely be challenged on the basis they have previously argued how important it was to have a separate space for “women” (however they’ve defined it) where men can’t go.
Obviously, there would be plenty of other grounds to challenge an organisation converting a women’s space to a mixed one, but I think it will be particularly difficult for the orgs who’ve made high profile arguments that TWAW and that “women” need their own space away from men.