I'd be less relaxed if I were you Rat
Under aspects of transitioning
Social The trans person makes changes to their social life and environment. For example, they may:  Begin to tell people about their gender identity, such as work colleagues;  Express their gender identity through changes in their clothing or hairstyle;  Ask to be referred to as ‘he’ or ‘they’ rather than ‘she’ or vice versa;  Start using toilets and other single-sex facilities that match their gender identity;  Use a different name;  Change their gender, title and name on documents such as credit cards, bank statements, utility bills, medical records and employment records.  Change their gender, title and name on government-issued forms of identification.
And this example, which I find bizarre, on "separate" sex provision
A service provider can deliver separate services for men and women where providing a combined service would not be as effective. In each case, such provision has to be justified. So, for instance, it would not be unlawful for a charity to set up separate hostels, one for homeless men and one for homeless women, where the hostels provide the same level of service to men and women because the level of need is the same but a unisex hostel would not be as effective.
I assume effective does not mean "is safer for women having conducted an equality impact assessment"