AuroraSaab
Squire
Jeez, we've explained this several times over.
The 'in law' bit refers to the Gender Recognition Act 2004. If one can jump through the required medico-legal and practical hoops then you can have a birth certificate in your acquired gender. The UK was dragged kicking and screaming to pass that legislation because being unable to marry was a breach of people's Human Rights.
But this is not what transactivists want. It's not what Stonewall want. They want all the exemptions of the Equality Act to be removed. That means there are no longer any single sex spaces or services (for either sex) from which the other sex can be lawfully excluded. It's just self ID into those spaces and services, no GRC needed.
You seem to be under the impression that admittance to these spaces and services will be limited to those with a GRC who have somehow 'earned' the right to be in those spaces. That simply would not be the case if 'sex' is overwritten with 'gender' in UK law.