@DadJoke You can argue that transwomen are women until you are blue in the face but the Equality Act doesn't agree. If TW are W there would be no need for Schedule 3, Part 7, Paragraph 28 in that act.
Talking of the Equality Act, you have been trying to persuade us that excluding transwomen from the Ladies' pond would be unlawful under the EA and its associated statutory guidance. This is link to the EHRC guidance on sex and GR exceptions for service providers:
www.equalityhumanrights.com/sites/default/files/guidance-separate-and-single-sex-service-providers-equality-act-sex-and-gender-reassignment-exceptions.pdf
Careful reading of this guidance reveals that:
1 - excluding people with the PC of GR from a single sex facility is a proportionate means to achieve the legitimate aim of allowing access to people who would otherwise be prevented by their religion if a mixed sex facility is also provided.
2 - excluding people with the PC of GR from a single sex facility is a proportionate means to achieve the legitimate aim of protecting the dignity and privacy of that sex if a mixed sex facility is also provided.
3 - excluding people with the PC of GR from a single sex environment without providing a mixed sex alternative is not necessarily unlawful providing that there is a reasonable balance of impact on competing protected characteristics. If exclusion would cause a detrimental impact on 1,000 people with the PC of GR but cause a positive impact on 4,000 people with the PC of religion (practicing Moslems or Orthodox Jews) then that exemption would be lawful. The service provider would need to conduct an accurate survey to justify exclusion on this basis.
4 - there is no requirement to show that a majority of service users would benefit from the exercise of an exemption to exclude people with the PC of GR. A single letter or email from a woman who believes that including men with the PC of GR would remove her dignity or privacy or from a single Muslim or Orthodox Jewish woman who states that the presence of a biological man prevents her from accessing the service is enough for the provider to review their policy.
5 - any single sex provider who fails to justify their policy of allowing people with the PC of GR to use the facilities that they choose when challenged by a user from 4 will probably be acting unlawfully.
Readers may find it useful to retain the link to the guidance for the next time somebody tries to use Stonewall Law to justify men's access to women's single sex spaces.