littlecabbage - under the GRA, a GRC (or being in the process of applying for one) gives a transperson the right to be treated in law as if they were a member of the opposite sex, except for a small set of exclusions where it would be considered to be proportionate to achieving a certain aim to limit access/employment to people of a certain sex.
So, for instance, places where women get naked, like open-plan single sex changing rooms - proportionate to exclude transwomen.
Women's prisons - proportionate to exclude transwomen.
Women's sports - left up to individual sports' governing bodies, but the point is they are legally allowed to exclude transwomen if they feel this is necessary in the interests of safety and fairness.
Both Stonewall and Jeremy Corbyn (among others) are on record as saying the Equalities Act is the next thing they will look at, after reforms to the GRA.
So it's a kind of pincer attack. Phase 1 - get rid of "gatekeeping", replace it with self-ID, so not just transsexuals with gender dysphoria get treated as legally women, but anyone who feels like signing a notarised piece of paper. At this point the cheerleaders for self ID say "it's okay women, don't get your knickers in a twist, it's just a change to the way the law is administered, you'll still have your protections under the Equalities Act."
Then, boom, phase 2. Repeal the relevant bits of the Equalities Act. That's the long (actually short-to-medium) term aim of the "transwomen are women" brigade.