One list of grant making bodies is at :
www.educational-grants.org/
To be honest, almost all are for children already in the private sector whose families suffer a crisis in income (e.g. death of breadwinner) and the charities will help out until the next stage in their schooling (i.e. if 14 will pay through GCSEs but not through A levels). Some may be more flexible, so worth looking. She may also get somewhere if she can show that a private school is not just a 'good thing' for her daughter, but essential to meet her daughter's exceptional educational needs. Also if accademically / musically brilliant, she may win a part-scholarship.
Queen Ethelburger's School also came up in a quick search as offering grants - that's yorkshire, no?