PTD Yes. That is just not true. A mixed sex service can be run which includes both cis and trans women but not men, without it being direct discrimination against men. But it may be indirect discrimination against women if there are no separate single sex services.
PTD is misleadingly incorrect here. Notice he refers to a mixed sex service in general. The Judge was referring specifically and only to lavatories:
Here's paragraph 61 from the Judgment.
Whether different treatment is also less favourable treatment is, therefore, a qualitative question. In a case where the provision of separate lavatories labelled male and female was materially similar in terms of the extent of the provision, location, and so on, I consider there would, in principle, be scope for a strong argument that a rule or practice that permitted trans women to use the “female” lavatory but required other biological men to use the male lavatory would comprise different but not less favourable treatment on grounds of sex. However, the circumstances of the case would be decisive. (For the purposes of the EA 2010 the lavatory would be mixed-sex, but for the purposes of the Claimants’ submission in this case it would still be labelled “women”.)
I do not think it is true to say in general that "A mixed sex service can be run which includes both cis and trans women but not men, without it being direct discrimination against men. " It would surely depend very much on the nature of the service.
If the service is provision of toilets then it is, truly, hard to see how a man denied access to women's toilets could claim discrimination - he doesn't have any proper purpose for being in a women's toilet. But if the service were a swimming pool then he could easily argue he's denied (for example) the opportunity to swim with his wife or daughter. This is very much the reasoning in al-Hijra, if anyone else is familiar with that case.