We don’t have self ID, yet
In all but name we do, under the tories.
https://gic.nhs.uk/info-support/gender-recognition-certificate/
Once you have a GRC you will be able to obtain a replacement birth certificate with your preferred (and now new legal) gender on it. Your pensionable age will be the same as your legal gender, and all of your legal rights and responsibilities will correspond to your legally updated gender
96% of people who ask for a GRC, get one, almost 500 last year... its obviously not quite self ID but considering the success rate in getting one, near enough...
Protecting womens rights.. ok.
Personally i think its ridiculous but i also think, as Blossoms said, if you can pay the rent, i don't whether it ll be an issue for you.