This is the current status quo and has been clearly established in recent legal cases (AEA vs EHRC most notably, as well as the High Court judgement on trans women in prisons).
AEA vs EHRC has no bearing on other cases because it set no legal precedent. It established nothing, in other words. As the argument and reasoning of the judge was distinctly illogical, I expect that a similar case would end differently (the judge was saying for instance that AEA's argument was absurd, because if it wasn't they would be right. That's astonishingly circular reasoning. The Legal Feminist blog has an excellent article on that called Schrödinger's PCP.)
Most importantly however, there is something that most commenters from the self-id side of the debate keep forgetting:
The EHRC stated in court that blanket trans exclusion policies are not in compliance with the statutory code.
And the code says that organisations really need to have a good reason to exclude people with the protected characteristic of gender reassignment from their service.
Yes, they did say that, and this is emphasised and celebrated by BlueberryCheezecake & friends.
The EHRC also stated that blanket trans inclusion policies are not in compliance with the statutory code either.
And the code does say that organisations must carefully consider the detriment to other service users if a member of the opposite sex is included in a single-sex service and the service must balance the rights of both, and not merely prioritise the needs of people with the protected characteristic of gender reassignment.
(In practice this means a service can exclude them outright, but it would be preferable for them to offer an alternative provision to people with the protected characteristic of gender reassignment that means they don't have to use the space provided for their own sex but which excludes them from the space provided for the opposite-sex. That would be legal, legitimate and proportionate.)
Yes, the EHRC really did point that out. I'm sure we're all just meant to ignore that though.