The EqA still applies to schools, and the CoP references employment in schools, which has direct revelance to this issue, though there are some exceptions. So, anything in the guidance which suggests trans boys should be forced to use girl's toilets, or that transgender teachers should be outed are not permitted.
The current EHRC schools technical guidance says, for example:
A previously female pupil has started to live as a boy and has adopted a male name. Does the school have to use this name and refer to the pupil as a boy?
Not using the pupil’s chosen name merely because the pupil has changed gender would be direct gender reassignment discrimination. Not referring to this pupil as a boy would also result in direct gender reassignment discrimination.
A school fails to provide appropriate changing facilities for a transsexual pupil and insists that the pupil uses the boys’ changing room even though she is now living as a girl.
This could be indirect gender reassignment discrimination unless it can be objectively justified.
Schools Week (not a trans rights organisaton) mentions some of the legal problems.
Meanwhile, today’s guidance states, as one of five key “principles”, that there is “no general duty to allow a child to ‘social transition’”.
But the legal advice from government lawyers said there was a “high risk of successful challenge to the guidance on the basis that this statement is misleading / inaccurate”.
Lawyers also warned of a “high risk of successful challenge to guidance or schools” in relation to a passage stating that “as a default, all children should use the toilets, showers and changing facilities designated for their biological sex unless it will cause distress for them to do so”.
I'm sure that we all agree that the guidance needs to be lawful, whatever objections you might have to the law.
https://schoolsweek.co.uk/trans-guidance-dfe-lawyers-said-schools-face-high-risk-of-being-sued/