@OldCrone
The statutory guidance from EHRC, which courts need to follow unless they have very good reason not to, states:
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.
So this is the starting position. Trans people have to be treated in the gender role in which they present in the case of single sex services unless they fit into the exemptions.
The code then goes on to say
^13.59
Service providers should be aware that where a transsexual person is visually
and for all practical purposes indistinguishable from a non-transsexual
person of that gender, they should normally be treated according to their
acquired gender, unless there are strong reasons to the contrary.
This is then a warning that in this case a trans person is unlikely to fit into an exemption. The "visually and for all practical purposes" comes from case law. It was the standard the courts applied to defacto recognition of the new gender prior to the GRA.
The quotes that @OldCrone come from general guidance (which does not need to be followed by the courts).
The entire section is
Generally, a business which is providing separate services or single-sex services should treat a transsexual person according to the sex in which the transsexual person presents (as opposed to the physical sex they were born with), as it is unlawful to discriminate against someone because of gender reassignment. Although a business can exclude a transsexual person or provide them with a different service, this is only if it can objectively justify doing so.
^A business may have a policy about providing its service to transsexual users, but this
policy must still be applied on a case-by-case basis. It is necessary to balance the needs of the transsexual person for the service, and the disadvantage to them if they are refused access to it, against the needs of other users, and any disadvantage to them, if the transsexual person is allowed access. To do this may require discussion with service users (maintaining confidentiality for the transsexual service user). Care should be taken in each case to avoid a decision based on ignorance or prejudice.^
Where a transsexual person is visually and for all practical purposes indistinguishable from someone of their preferred gender, they should normally be treated according to their acquired gender unless there are strong reasons not to do so
^Where someone has a gender recognition certificate they should be treated in their
acquired gender for all purposes and therefore should not be excluded from single sex
services.^
It is clear in this non-statutory guidance that the "visual and practical purposes" test and the GRC are warns about the exemptions in the EA.
So trans people do have the right to use single sex spaces (in effect sue under the EA for discrimination) without a GRC or meeting the "visual and practical purposes" test.