I post this with the awareness that there will be many people who disagree with me, and that's fine. I feel it is important to post accurate advise and to provide alternative views, which I've been assured are welcome on Mumsnet.
The reason why we disagree with you DaisyJohnson is because what you posted is not advice, let alone lawful advice, but uninformed nonsense.
You make up very odd rules about disclosure and you refer to the Equality Act 2010 as if this was the only relevant legislation.
If you really are a teacher, then you will no doubt be aware that safeguarding children is something so important that we don't just have one relevant law, or two, or three, but nine different sets of laws which inform how safeguarding works in UK schools.
The Children Act 1989
The United Nations Convention on the Rights of the Child 1992
The Human Rights Act 1998
The Education Act 2002
Equality Act 2010
Children and Families Act 2014
The Children and Social Work Act 2017
Working Together to Safeguard Children 2018
Keeping Children Safe in Education 2019
We look to all of these different laws to balance the need to safeguard children with the rights they have under these laws. So, no, the rights of a child under the Equality Act 2010 do not supersede the rights of its parents to make decisions they believe to be in the child's best interest, even without the consent of the child.
As an example of how these laws inform our safeguarding policies, I already quoted in an earlier comment on this thread an excerpt from a Children's Rights Impact Assessment on the withholding of information from parents that shows how this potentially violates the rights children have under the UN Convention on the Rights of the Child.
FYI, this assessment was scrutinised by the Children's and Young People's Commissioner in Scotland (CYPCS). This is the regulator tasked with upholding children's rights in Scotland. (England and Wales have their own Commissioner.) The CYPCS not only accepted the assessment was accurate, they publicly called it “extremely thorough, well researched, comprehensive, informative and helpful”. They then contacted the Scottish Government to remind it that all guidance used in schools must be lawful (said guidance incorrectly claims amongst a great many other incorrect claims that information of a child's trans status must be withheld from parents if the child doesn't consent to sharing it). The Scottish Government later got separate legal advice on its preferred guidance, which confirmed that it was "not legal".
Please consider what everyone else involved in safeguarding has told you - an important safeguarding principle is not to promise confidentiality to a child. What they have also all pointed out is that any disclosure that raises a safeguarding concern is then referred to the school's safeguarding lead (and not immediately and automatically shared with parents).