This is interesting:
"School leaders have said that, without national guidance on transgender issues, schools are left relying on lobby groups."
Not just schools perhaps. Without clear government guidance all sorts of institutions may have been forced to rely on lobby groups.
The very good news is that the GDST (Girls Day School Trust) appear to have sought legal advice and come to the conclusion that the single sex provisions in the Equalities Act are important, as it is these provisions that allow them to deliver single sex education.