They say they would have an obligation to a transgirl under the Equality Act 2010 to put them in with the girls
No such obligation exists. Ask them to point you to the part of the EA that outlines this obligation, they will not be able to.
What I'm slightly uncertain about is the gender reassignment characteristic in the EA 2010. Could they argue that trans comes under that? We are talking teenage male child who identifies as a girl here, not anyone who has had surgery or with a GRC.
This male child probably does have the protected characteristic of gender reassignment. You don't need surgery, you don't need a GRC, there's no age limit. The minimum requirement is that you are proposing to undergo part of a process for the purpose of reassigning your sex by changing non-physiological attributes.
www.legislation.gov.uk/ukpga/2010/15/section/7
Probably a male child saying 'I identify as a girl' is enough to have that PC. Nevertheless it doesn't change the child's sex, biologically or legally.
The relevant exception that makes single sex accommodation lawful in the first place is found in Schedule 23, paragraph 3:
www.legislation.gov.uk/ukpga/2010/15/schedule/23/crossheading/communal-accommodation
It is lawful to provide single sex accommodation and to exclude all legal males from female accommodation, whether or not they have the protected characteristic of gender reassignment.
The gender reassignment exceptions only apply in areas where there is already a single sex exception in place and are only necessary where someone has legally changed sex.
Subparagraph 4 says in relation to gender reassignment, account must also be taken of whether and how far the conduct in question is a proportionate means of achieving a legitimate aim.
The 'conduct in question' is providing single sex accommodation.
Preventing harassment is always a legitimate aim because harassment is prohibited conduct under the EA.
Harassment is when a service provider, employer, public authority bla bla engages in unwanted conduct (e.g. implementing a 'trans inclusion accommodation policy') related to a protected characteristic (e.g. sex) that violates your dignity or which creates an intimidating, hostile, degrading, humiliating or offensive environment for you.
www.legislation.gov.uk/ukpga/2010/15/section/26
If everyone has their own en-suite room it would be difficult to argue that anybody's dignity has been violated but I think you could argue that an intimidating, hostile and offensive environment had been created for you, if you were a female student in this situation.
Helen Saxby:
It’s sometimes difficult to remember, amongst all the arguments, exactly what women stand to lose here. The sex category ‘female’ is being asked to absorb the sex category ‘male’. What women are being forced to accept could literally not be any more extreme.
notthenewsinbriefs.wordpress.com/2017/11/26/when-womens-rights-are-notadebate/
Excluding male people, even if they are legally female, from female only space is always a proportionate means of preventing unlawful harassment of female customers, employees, service users bla bla, because allowing just one male person into female only space makes it mixed sex for everyone.
As this is to do with children then safeguarding law will also have lots to say. That's not my area of expertise. I miss langcleg's wonderfully clear posts on safeguarding.
We have no legal right as individuals to insist that a single sex exception is used. We do have a legal right to insist that we are not harassed and that children are safeguarded.