Further reading and resources
Single Sex and Separate Sex Facilities
ECHR statutory guidance on the operation of the Equality Act 2010 in the provision of Services and Public Function.
Paragraphs 13.57 – 13.60 cover the operation of single-sex spaces. Statutory guidance is not the law itself, but it “shall be taken into account by a court or tribunal” (s. 15(4) Equality Act 2016) and per Baroness Hale speaking in the House of Lords in (SCA Packaging v Boyle  UKHL 37 para. 67).
Gym Use and Changing Rooms: the illegality and chilling effect of (trans)gender segregation:
Peter Dunne and Alex Sharpe
Article on the unlawfulness of having blanket bans on transgender women using gym changing rooms
Failed Challenge to Trans Equality Guidance around Single-Sex Spaces
Anti-trans group's attempts to launch a process to have trans people excluded from single-sex spaces fails because it has no legal merit:
A letter from TLP, signed by 39 legal/academic and associated professionals challenging recent guidance issued by them which encouraged interpretations of equalities law to include pre-emptive, blanket bans of trans people. Plus:
EHRC reply to above letter
Croft v Royal Mail 
This landmark case concerns the right of a transgender woman to use the toilet at work. Though almost 20 years old we believe that the legal test stated remains accurate. https://www.bailii.org/ew/cases/EWCA/Civ/2003/1045.html
Taylor v Jaguar Land Rover 
A groundbreaking case recently decided at the Employment Tribunal. The tribunal held that non-binary people are protected by the EA 2010 and requiring a non-binary person to use the disabled toilet was direct discrimination. Jaguar Land Rover has accepted the judgment and is not appealing.
The recruitment and retention of transgender staff: Guidance for employers: Government Equalities Office
Probably the best non-technical guide. Page 14 covers single-sex spaces.
Protection from discrimination for transgender individuals in UK law
Substantive review of Taylor v JLR
EHRC Policy Position 2021-2022
In 2021, the EHRC reversed its previous long-standing support of trans rights across a range of issues.
Correspondence here is between Trans Legal Project and the EHRC 2021-22, focussing on separate and single-sex spaces.