Perhaps you're right. IANAL. I don't know what the exact facilities were in the M&S in the video.
But I know that Sex Matters have complained to M&S for providing mixed-sex changing rooms and no women-only. https://sex-matters.org/posts/single-sex-services/ms-warned-mixed-sex-changing-rooms-could-be-unlawful/
I also know that WRN has identified at least one M&S store, in Shoreham-by-sea, which has a men-only changing room, a mixed-sex one, but no women-only.
Naomi Cunningham posted yesterday on X suggesting that men-only toilets but only mixed-sex ones available for women is 'direct discrimination against women' (in a discussion about the Barbican).
(Link below to her thread via nitter. The Barbican Centre not the ideal example as it does have women-only as well).
P.S. I wasn't 'proposing' (as you claim) that the M&S video woman should bring a claim, - I don't know this woman! - it was just by way of an example, perhaps a bad example, so I apologise for misleading anyone. I think it was more seeing that the guidance said that a company could be liable for unlawful actions by its employees, and the M&S male staff member sprang to mind.
If you read the Sex Matters advice, it is very detailed and provides clear examples. The process for making a claim is quite lengthy and I doubt anyone would bother to pursue one if they weren't sure the claim was solid, and I certainly wouldn't recommend claiming if you weren't sure.
https://nitter.net/LoudBonnet/status/2061393455683686806#m