Has she missed any school?
Your school should have an emotionally based school avoidance procedure. Emotionally based school avoidance absence should be documented separately to normal absence and should follow a different absence procedure.
If she's missed more than 15 days of school either cumulatively or consecutively because of her anxiety and struggles around school you can also write to the LA.
You can state:
My child has now missed 15 days of education due to emotionally based school avoidance. Under section 19 of the Education Act, I understand the local authority has a duty to provide a suitable full time education. This setting is no longer suitable. Please confirm the provision you will be putting in place.
Alternatively if she doesn't have an EHCP, nows the time to apply for one, which will include a needs assessment. You can either wait for an appointment with an educational psychologist they appoint or hire a private one which may be quicker and their feedback report can be used in an EHCP.
Ultimately you're trying to prove this school can't meet need, irrespective of funding, and needs a specialist provision. You may need SEND guidance from SENDIASS who can provide advocacy services. They claim to be impartial but they are government appointed so it's essentially the second hand to the local education authority who will try and do anything to not fund a specialist placement where they can get away with it. Alternatively there are other services like IPSEA or SEND SOS.
You can also request Education Other Than At School (EOTAS) in the interim, which can also be a battle as everything we do for our SEN children so unnecessarily is, and it can be done on a permanent basis or you can request it as an interim solution while they source an alternative/specialist provision.
This is NOT electively home educating, so it keeps the LEA on the hook for making sure they find her the right placement whereas EHE gets them off the hook.
I know that's a lot of information to digest but I hope it's given you some direction.