While I was looking for the quote and the link to the EA2010 about how single sex services might be affected by someone with the protected characteristic of gender reassignment I came across this thread. The post by Thistledew on Mon 17-Sep-18 at 00:08 sets out the problems of how the two protected characteristics might come into conflict in this sort of situation (I hope my link will go straight to the right post).
I also found this government report about Transgender Equality which refers to the example of the women-only group counselling session in the EA2010. The example as it is stated in the EA2010 doesn't specify whether the transsexual person holds a GRC or not.
This is what Claire McCann, a barrister, said:
124. Ms McCann advised us that “this example is drafted too categorically”. While it demonstrates a “legitimate aim”, it gives “insufficient information […] to show that the exclusion of trans people is appropriate and reasonably necessary (i.e. proportionate) to meet that aim”. She further suggested that in the instance cited it may only be lawful to exclude trans people if they do not hold a GRC:
"I would doubt that a service-provider of single-sex or separate services could turn away a trans service-user who holds a GRC because this is unlikely to be proportionate."
It seems that it may be impossible to exclude a GRC holder from single-sex services and spaces which are designed for people of the sex which the GRC holder now has in law.
This is why self-ID is a problem, and why single-sex provision in the EA2010 is incompatible with a GRA which allows self-ID. (It is also incompatible with the GRA as it currently stands, but at least there is some gatekeeping, and a tiny number of GRC holders).