I disagree with Karon about self-ID having no impact, although, I do see why she says that and she makes a very good point about the lack of guidance being the real problem.
And actually, having read this all through, to my mind self-ID will just lower the threshold for when it's reasonable to use the Equality Act 2010 exemptions for a strictly single-sex space. Which could be a good thing.
For example, when a GRC needed a Gender Dysphoria diagnosis, and most had had surgery, then it might not have been proportionate to exclude a transwoman from, eg, a female changing room, (but a rape crisis centre would be OK).
However, if GRCs are done on self-ID basis with most holders having no medical treatment, then it becomes necessary and proportionate to exclude transwomen from changing rooms too (as more women will feel frightened or uncomfortable being in a changing room with someone who they perceive to be a man, whereas they may not have if it was a dysphoric post-surgery transwoman).
But a really interesting and insightful read. It gives me hope that any changes in the GRA will be alongside much more promotion of, and comfort using, EA exemptions.