but the supreme court is another matter entirely?
No all of these court case are about how the Law is written. As I said up thread, as both earlier cased showed, if Judges just strictly look at the words which say "for all purposes" a man with a GRC is a woman (and the tiny tiny concession which shows they know he really isn't) exempt under the limited occassions under the Single Sex Exemptions).
Can the High Court say that a Law is badly written, ie instruct Parliment to rewrite a Law?
Have just seen this:
Section 4 of the Human Rights Act says that if a higher court (such as the High Court, Court of Appeal or Supreme Court) considers that part of an Act of Parliament is incompatible with human rights, it can make a declaration of incompatibility.
https://www.libertyhumanrights.org.uk/your-rights/the-human-rights-act/how-the-human-rights-act-works/