You can't have a men-only bar, or a women-only train, or a men-only construction site because those things would be discriminatory on the basis of sex.
You can... if you can demonstrate it's a "proportionate means of achieving a legitimate aim".
So potentially, a men-only bar for same-sex attracted might meet this criteria e.g. there might be enough gay men feeling fed up that straight females are identifying as gay men and are insisting on accessing gay men's social spaces.
Likewise, a women-only train (carriage) might meet the criteria on safety grounds, if there is data to suggest that mixed-sex carriages are a risk.
Equally, they might not. It's about demonstrating why it's legitimate to discriminate on the basis of sex. In some cases it's much easier to demonstrate why it's needed e.g. male and female sports categories. IIRC discrimination on the basis of sex for sport is specifically mentioned in the EA. Perhaps because it's one of the easiest legitimate reasons to articulate.
Without the SSE, it would be impossible to have any single sex spaces, services and associations (except sport, because it is specifically mentioned).
As PPs have said, the SSE is needed. What's at stake here is whether a GRC allows someone to "be" the opposite sex under the SSE.
@IwantToRetire do you agree that it should remain lawful to discriminate on the basis of sex, where it is a proportionate means of achieving a legitimate aim - e.g. having changing rooms separated by sex for the purposes of dignity and safety? If so, this means you support the SSE....