Returning to the unfortunate
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 can't see how it would not contravene the EA2010 to allow some males to use the 'Women's' but not others.
The Supreme Court said that even holding a GRC does not make a man a woman in the context of the EA, and therefore no man, GRC or not, is entitled to use the women's facilities.
Purely on the grounds of logic, how is it legally 'discriminatory' to require a transperson to use the toilet designated for their biological sex?
They have no right to use the opposite sex toilet, even if they have a GRC.
They are not being deprived of toilet facilities. It's not like they need adaptations to use the toilet designated for their sex, they just choose not to use them because they feel uncomfortable using them.
They might not like it, but is that really, legally, discrimination?