@WhatNextCatsAsDoctors I think you need to look at Schedule 16 to the Equality Act. This is the provision that deals with the exception for associations. The effect of paragraph 1(1) is that it is lawful for an association to restrict membership to 'persons who share a protected characteristic'. That means that everyone who is a member needs to share the same protected characteristic and therefore, if two or more protected characteristics are involved, all members need to share all the relevant protected characteristics. Otherwise the association would be unlawfully discriminating - as others have said.
An association for disabled women would be entitled to restrict its membership on grounds of sex (all member would be women) and disability (all members would be disabled).
An association for disabled people AND women would not be possible without unlawful discrimination against non-disabled men, because non-disabled women were allowed to join so it is sex discrimination not to open membership to non-disabled men. Disabled people and women do not share the same protected characteristics.
An association for male trans people (i.e. transwomen) would be entitled to restrict its membership on ground of gender reassignment and sex.
An association for women and transmen would be entitled to restrict its membership on grounds of sex because transwomen are female.
But an association for women (adult human females) and transwomen (male trans people) could not exist because women and transwomen do not share the same protected characteristics.
For the avoidance of doubt, I have read the Supreme Court judgment in full; have read the relevant sections of the Equality Act; have several decades' experience working with statutory law; and do not get my legal knowledge or advice from lobby groups.
https://www.legislation.gov.uk/ukpga/2010/15/schedule/16
Edited to tag the PP - my attempt at quoting PP failed.