@OldCrone
Their sex (the sex which is legally recognised) isn't 'irrelevant' to single sex spaces. If sex was irrelevant for single sex spaces there couldn't be any single sex spaces. Both the protected characteristics of sex and gender reassignment are relevant.
Take the example of a women-only space. Men are excluded. Anyone who is male (legally male) is excluded. Someone born male who identifies as a woman but doesn't have a GRC is legally male, so he is excluded on the basis of his sex, just as any other man is excluded on the basis of his sex. He is not treated any differently from any other male person, so there is no discrimination due to the protected characteristic of gender reassignment.
A woman who identifies as a man but has no GRC is legally female, so cannot be excluded from a female-only space. To exclude such a person would be to discriminate because of gender reassignment, so she shouldn't be treated any differently from any other female person.
A person born male who has a GRC is legally female, so would normally have the right to enter female-only spaces, but there are still provisions in the EA to prevent this if it is a proportionate means of achieving a legitimate aim.
The comparator for discrimination on the grounds of gender reassignment is with someone of the same legally recognised sex.
I’m still not sure this is correct. Obviously in establishing a single sex service the provider has to show that the conditions for relying on the sex discrimination exception are met. And it may well be right to say, as the EHRC does, that where a trans person brings a sex discrimination claim, their sex for that purpose will be their legal sex, which will depend on whether they have a GRC. But everything I’ve read indicates that a trans person with or without a GRC could potentially challenge their exclusion from a single sex service on grounds of gender reassignment discrimination (and ultimately the lawfulness of their exclusion will be very fact specific) - if it were enough for the provider to simply say ‘you don’t have a GRC, so your legal sex is male, and therefore we are excluding you like any other man’ then how could a trans person without a GRC ever bring a gender reassignment discrimination claim in those circumstances?