Is this the same school as the other thread (King Edmund Academy)? If so, my views are below. If not, then there is a different set of Regs which oblige the school to provide single sex bathrooms which might apply depending on the type of school (the ones below apply to academies), so some of the references would be wrong but the principles are the same. Sorry if the following is a bit long!
School's breach of obligations re: toilets
The school is breaching para 23 of the Schedule to the Education (Independent School Standards) Regulations 2014 by failing to provide separate toilets for boys and girls aged 8 or over (www.legislation.gov.uk/uksi/2014/3283/schedule/paragraph/23/made). The above is on my assumption that school is allowing the trans child to use ordinary cubicle toilets - if on the other hand the toilets in question are in a fully enclosed room with a single toilet those can be unisex without breaching the Regs.
Gender Recognition Act 2004
It is not possible to legally change your gender by obtaining a gender recognition certificate using the process in the Gender Recognition Act 2004 until you turn 18. Therefore, the child will be regarded in the eyes of the law as a boy who wishes to transition, rather than legally being a girl for the purposes of the Independent School Standards Regs mentioned above.
Equality Act 2010
Contrary to what I understand Transpire have said, the Equality Act 2010 does not require the school to allow a pupil to use the toilets which they feel comfortable with.
The Equality Act is a bit weird hard for people to get their head around at first but basically work by having a list of protected characteristics (sex, race, disability, gender reassignment), some different contexts (eg employment, services, education) and prohibited behaviours.
So the school will say that the trans child has the protected characteristic of gender reassignment on the basis that the child is proposing to go through a process to reassign there gender.
The relevant bit of the Equality Act is s85(2) www.legislation.gov.uk/ukpga/2010/15/section/85 which sets out that schools must not do the following in relation to someone with any protected characteristic (including gender reassignment). It says:
The responsible body of such a school must not discriminate against a pupil—
(a)in the way it provides education for the pupil;
(b)in the way it affords the pupil access to a benefit, facility or service;
(c)by not providing education for the pupil;
(d)by not affording the pupil access to a benefit, facility or service;
(e)by excluding the pupil from the school;
(f)by subjecting the pupil to any other detriment.
In the context of transgender pupils, this does not mean that the school is required to allow the pupil in question to use the facilities of their choice. What it means is that:
A) The school can allow the pupil to use a unisex bathroom if there is one. As above, this must be a self-contained bathroom in a room of its own. I know that in a lot of similar instances trans pupils are allowed to use the staff bathroom as these are often unisex self-contained bathrooms.
B) The school could still force the trans child to use the bathroom that corresponds to their sex if it is 'objectively justified'. The test for objective justification is whether the action is proportionate means of achieving a legitimate aim (ie in very basic terms, there's a good reason for the discrimination and the discrimination is kept to the minimum realistically possible). In this context, I think that there would be a legitimate aim of complying with the legal requirements of the Independent School Standards Regs mentioned above and maintaining the privacy/safety of female pupils. However, it would only be proportionate to do so if there were no unisex toilets on site (and arguably only for a limited period as the school could put in a single unisex toilet).
The Equality and Human Rights Commissions guidance is useful here as the school should be using this, rather that whatever guidance Transpire is putting out. www.equalityhumanrights.com/sites/default/files/technical_guidance_for_schools_england.pdf Whilst it doesn't cover toilets, it does give an example re: trans use of school changing rooms in the example box below para 3.20. The exact same principles apply to toilets.
If there is anything further that I can do at all to help in relation to this do let me know. I am very happy to help!