Saga there is an exemption in the EA (which I just posted) that permits single sex services to exclude trans if it is a proportionate means of achieving a legitimate aim. This is currently the same whether the person has a GRC or not. It's not surprising if you are unaware of this exemption because vanishingly few service providers have the guts to use it these days.
Miller's report, BTW, recommends getting rid of this exemption:
Exemptions in respect of trans people
21.Significant concerns have been raised with us regarding the provisions of the Equality Act concerned with separate-sex and single-sex services and the genuine occupational requirement as these relate to trans people. These are sensitive areas, where there does need to be some limited ability to exercise discretion, if this is a proportionate means of achieving a legitimate aim. However, we are not persuaded that this discretion should apply where a trans person has been recognised as of their acquired gender “for all legal purposes” under the Gender Recognition Act. In many instances this is unlikely, in any case, to meet the proportionate test. (Paragraph 132)
22.We recommend that the Equality Act be amended so that the occupational requirements provision and / or the single-sex / separate services provision shall not apply in relation to discrimination against a person whose acquired gender has been recognised under the Gender Recognition Act 2004. (Paragraph 132)
At the same time the report recommends changing the GRA to self-ID (which is what is about to be consulted on):
7.Within the current Parliament, the Government must bring forward proposals to update the Gender Recognition Act, in line with the principles of gender self-declaration that have been developed in other jurisdictions. In place of the present medicalised, quasi-judicial application process, an administrative process must be developed, centred on the wishes of the individual applicant, rather than on intensive analysis by doctors and lawyers. (Paragraph 45)