The protected characteristic of gender reassignment applies to all, children and adults, who propose to, are undergoing or have taken steps to transition. This includes a social transition.
So your pupils are protected under this characteristic of gender reassignment.
The only protected characteristics that do not apply in schools are age and marriage and civil partnership.
However, no child under 18 can legally change sex. So when deciding access to changing rooms or toilets, no child can have a gender recognition certificate and so only has to be compared with a child of their own sex if you want to find out if they're being treated unfairly.
Say your school had a special program designed to keep the oldest girls interested in science, and you had a male child who identifies as a girl saying that its unfair they cannot participate. You would only have to show that all male pupils are excluded, this child is both legally and biologically male, so this is not unfair. (Ideally schools would find a solution that also supports this child, but legally the child cannot insist on joining that program for girls.)
But if the same child comes to you and says the boys are bullying me in the changing room, because of my identity, the school would be discriminating against the child on the basis of gender reassignment if management and teachers insisted on the child continuing to change with the boys. But please note, if the school bans the child from the boys' changing room they would also be discriminating against the child, this time on the basis of sex, because the school is not allowed to ban a male child from facilities provided for their own sex.
If the child then says I want to change with the girls and if the school allowed this male child to change with the girls, they would be treating the girls unfairly because girls have a right to single-sex facilities in school from the age of 8.
That's why the Equalities and Human Rights Commission, who are the organisation tasked with regulating the Equality Act 2010 by the UK Government, published Technical Guidance for schools in 2014 which recommends that the school provide an alternative changing area or an alternative time to change in the boys' changing room for the child (but only if the child does not want to change with the boys). They do not recommend letting a male child change with female children.
This guidance is not legally binding for schools, but could be used in evidence if a claim is brought against a school.
www.equalityhumanrights.com/en/publication-download/technical-guidance-schools-england
Furthermore, neither gender nor gender identity are legally defined terms under UK law and if your school ever had to defend against a claim of discrimination on the basis of sex, the court would take into account that the school did not have any policies in place designed to avoid discrimination on the basis of sex.
I spoke to someone at the EHRC as to whether it was allowed for public sector organisations to simply choose their own wording for the protected characteristics and they said absolutely not. It takes an Act of the UK Parliament to change the wording of the protected characteristics named in the Equality Act and if an organisation does not include the relevant ones, they could be in trouble if anyone brings a discrimination claim.
However, what organisations are allowed to do once they have listed the protected characteristics under the Equality Act 2010 is to add extra characteristics. So you'll find that some include education, class or socio-economic status, nationality etc.
HTH