This comment from The Times article illustrates my point:
Providers of women-only services [can choose not to] provide services to trans individuals, provided it is objectively justified on a case-by-case basis. The same can be said about toilets, changing rooms or single-sex activities“....
Prove to whom, how and in what circumstances?
There are no relevant forms of identification that are available or required to carried by those who are TG to identify their status. Requests to prove gender based on appearance and any request to prove the presence, or lack of, genetalia, would be fraught with the danger of both embarrassment and subsequent lawsuits.
I'm sorry for the dampener but it looks like a PR exercise to me