The EA2010 was published after the GRA, and allows providers to include or exclude people whose gender matches the single-sex space, subject to gender reassignment exceptions. People with a GRC also have that protected characteristic, and can also be excluded on that basis.
See the EHRC Statutory Code of Practice as confirmed in AEA vs EHRC.
13.57 If a service provider provides single- or separate sex services for women
and men, or provides services differently to women and men, they should
treat transsexual people according to the gender role in which they present.
However, the Act does permit the service provider to provide a different
service or exclude a person from the service who is proposing to undergo, is
undergoing or who has undergone gender reassignment. This will only be
lawful where the exclusion is a proportionate means of achieving a legitimate aim.
A transexual person is defined in the EA2010 as a person with the protected charateristic of gender reassignment.
This gender critical site summarises it, and bemoans that providers are not using the exceptions which are available.
At this stage the parties’ arguments essentially converged. Both parties were arguing that a GRC was not relevant to the provision of a single sex service.
https://www.legalfeminist.org.uk/2021/05/10/aea-v-ehrc-an-explanation/