AuroraSaab
Squire
The Equality Act 2010 provides a single, consolidated source of discrimination law. It simplifies the law and it extends protection from discrimination in some areas
The article I linked to is advice as to how the act should be applied in the context of education. If you read the Act itself it is very clear that schools are not allowed to discriminate based on gender identity. That is the law whether you like it or not. Thus, as I stated, it is clear that (as usual) Braverman is in ignorance of the law. This is not unusual for her. It is unusual for the Attorney General not to have a clue about the law as it's their actual job to advise the government on the law. But - as we know from Gove - they don't like experts.
Gender identity is not a protected characteristic under the Equality Act. Gender reassignment is, but it seems unlikely that a school age child under 16 could be said to be meeting the criteria for having reassigned their gender.
The document you linked is guidance, not law. It doesn't supercede the law. It confuses things though, which is why it's supposedly under review I expect.
When a male pupil who identifies as female is prevented from playing on the girls football team they are not being discriminated against because they are transgender. They are being excluded because they are male - which is legal under the Equality Act. If they weren't allowed to play on the boy's team because they identified as female, that would be being discriminated against because they are transgender.