So M&S & other stores absolutely could probably just say: We don't feel our staff can challenge any well behaved customer who is politely requesting access to a fitting room, even if we put up signage saying 'women' & 'men'. Accordingly, we aren't going to claim our changing rooms are single sex. They are not. They are unisex. As our clothing is laid out in 'women''s & 'men''s sections, we expect most people will go to the fitting room at end of the store that has clothes being primarily marketed to their sex...but we are not planning to stop a man who is peaceably bra shopping from trying things on in the facility nearest to the lingerie section.
I mean, they could. & women like me who don't fancy sharing the space will say: ok, I'll shop elsewhere, at a store that meets my needs.
OR they could say: We are following the SC judgment, our changing rooms are going single sex & staff will refuse entry to customers trying to access the wrong one. We fully support any of our customers who prefer not to use correct sex facilities to try items on at home & return them if they are not happy.
They just can't fudge it anymore, & call a fitting room a space for women if that isn't what it actually is. Nor can they claim they genuinely think Bra Buying Barry is a woman. The SC says he isn't.
I imagine how it'll pan out in the long run is that most businesses will adapt to the needs of their most profitable demographic, or they'll go under. Like pubs having to adapt due to cheap supermarket booze & the smoking ban.
As I said, M&S's stores in the ME have single sex changing, end of. They'll do what is most profitable AND keeps them out of court, wherever in the world they are. After the SC judgment, I would put a fiver on them wanting to keep their UK female customers happy.