CoteDAzur, if I'm skim reading this correctly www.equalityhumanrights.com/your-rights/equal-rights/transgender/transgender-what-the-law-says If they get a full gender recognition certificate, transgender people are legally considered members of the acquired gender in all ways, except for one important caveat about 'gender specific offences'. I guess that's to allow that transgender, erm, penised people (struggling with vocab here mn, no intent to 'offend') can still rape as that's classed as a gender specific offence. At least we have that.
But you then have as Harvey says the equality act which requires that transgender people are not discrminated against inthe workplace and vocational training, which it distinguishes from education, wrt
"recruitment, transfer, training and promotion, access to work-related benefits, facilities and services, dismissal, and any other detriment."
So I don't think that covers the use of public toilets, just the workplace ones.
The equalities act also covers women of course but there is no statement about what to do in the case of conflict. In UK I guess that would be left to precedent, which essentially boils down to what the judge felt like on the day. I have no legal training whatsoever but I think that's what they call a grey area in the law. Hope that helps, cos I'm still confused.