Thanks for the clarification @ChattyLion
Here are some incredibly brief thoughts on the law as I need to go do dinner.
The single sex exemptions allow service providers to provide single sex services in certain scenarios. But you have to have a justification for it and you cannot know for certain that it is justified unless someone sues you. Also there is zero case law on this, probably because any time anyone does threaten legal action the service providers cave very quickly, so you cannot really look at any other situations and see whether they were or we're not justified yet.
What there is is EHRC guidance. The EHRC guidance has to be taken into account in any legal cases so it is influential. I can find the link if anyone is interested but basically there's an example which is very YN helpful where they say that a clothes shop should let people pick the changing rooms that they like if they are self-contained.
I haven't see anyone using the indirect sex discrimination provisions to argue for single sex spaces. It's an interesting idea but my gut feeling is it would fail to be honest. It's open to the service provider to justify indirect discrimination and I think they could probably point to the fact that it can be quite hard to tell who is legally a man or a woman these days as there is no requirement to pass as the opposite sex to get a GRC.
The disabled angle is interesting. There are some specific disability related provisions in the Equality Act. I think though that the answer would be to get M&S to provide some better wheelchair accessible doors to replace the curtains, rather than keeping sex segregation.
Probably not what you all want to hear but it's my opinion on what the legal position is even if it sucks.