The GRA needs scapping altogether, because it no longer serves the tiny number of seriously dysphoric transexuals for whom it was designed, who wanted it for going incognito and allowing them to marry in a time when gay marriage was illegal. But this is very unlikely to happen.
Nowdays just about every transperson is out and proud, and corporate endorsement / biography pronouns are the norm - the number under the 'gender umbrella' is huge.
So allow people a GRC. Which states their Gender. And ensures they cannot be discriminated against because of it. Its a protected characteristic in the equality act.
But, as the TRAs and the woo-science tell us, sex and gender are totally different things, remove the ability to create a 'legal fiction' by changing a document that records biological sex. And uphold the single sex exemptions.