Reading through the judgment, I'm not sure I agree.
If you are providing a single sex space or service, you are only allowed to exclude the opposite sex if the rationale for having a single sex space satisfies the criteria in the Equality Act.
The judgment makes it clear that if you include members of the opposite biological sex who have a GRC in that single sex space, you are undermining the purpose of that space in the same way as if you included members of the opposite biological sex without a GRC in that space.
For example, if you set up a single sex rape crisis group for women, your legal right to provide that single sex service (which constitutes direct sex discrimination against men) depends on your ability to demonstrate that it is justifiable to provide a service to one sex and not the other, for one or more of the reasons set out in the Equality Act.
Paragraph 217 of the judgment says, "While many women in a female only changing room or on a women only hospital ward or in a rape counselling group might reasonably object to the presence of biological males, it is difficult to see how the reasonableness of such an objection could be founded in possession or lack of a certificate."
In other words, if you are providing a single sex space or service for women on the grounds that women may reasonably object to the presence of biological males, and relying on the exemptions in the Equality Act in order to directly discriminate against biological males, as soon as you allow some biological males to use that space or service (regardless of whether they have a GRC or not) you have undermined your entire justification for providing a single sex space or service in the first place. Because it is no longer serving its intended purpose from the point of view of its female users.
Annoyingly, the conclusion I am coming to here is not that women are entitled to single sex spaces or services, but that it is unlawful to provide a single sex space or service which excludes men if you are allowing trans women to use it.
My interpretation of this is that organisations can't be forced to provide single sex spaces or services, but that it is most likely unlawful to provide a single sex space or service that includes some members of the opposite sex on the basis of how they identify.
That means that organisations like the Survivors Network and Marks and Spencer need to shit or get off the pot. Provide a single sex space or service, advertise it as female only, and exclude trans women from it, or provide only mixed sex spaces and services so that at least everyone knows where they stand.
One concern I have is that many organisations may opt for the latter, leaving women with fewer single sex spaces than they have today. Because not every trans inclusive women only space will actually have trans women in it at any given time. So perhaps it is better for them to exist in their current form than not exist at all.
This is why I think Sarah Summers' case against the Survivors Network is going to be the next landmark piece of litigation. Because if I remember correctly, part of her argument is that rape crisis organisations have an obligation to provide single sex services because failure to do so constitutes indirect discrimination against women. I am not sure that she will win, but obviously I very much hope that she does. The Supreme Court judgment does help her case because it makes it clear that the Survivors' Network is advertising services as single sex when they are in fact not, and so has incorrectly applied the single sex exemption in the Equality Act. But will the court in that case go one step further and agree with her that not providing them constitutes indirect sex discrimination?