I believe it is still a criterion for changing gender to use the bathroom of the gender you are transitioning to for 2 years before the legal process can be satisfied. It sounds like the entire legal framework around changing gender is incompatible with requests like this.

For what it’s worth the supreme court decision simply found that someone’s sex could not be changed legally but that still shouldn’t preclude changing gender. Forbidding people from changing gender is essentially what is being asked for by these groups and society at large does not seem to have an appetite for that.

In the immediate future sex based legal protections do have the legal apparatus to trump gender based rights but it’s going to be implemented on an arbitrary, case-by-case basis. For example in the event that a trans person has a transphobic colleague of the same gender then the employer needs to provide facilities for both parties (as seen in a recent workplace dispute in Fife, Scotland). This is going to get messy where the NHS might have certain hospitals with this arbitrary need for extra facilities depending on people having the misfortune of transphobic colleagues.