Often the bright children get offers from several schools though so any figures regarding applications at schools (although perhapsnot Eton where it is likely to be the first choice of most applicants) look worse than they are.
This below from my daughter's old school North London C (day school fees about £12k a year seniors) is pretty consistent with what is mentioned above for academic boys' schools too.
"Bursaries & Scholarships
Central to the ethos at North London Collegiate School is the provision of bursary places to allow bright girls to benefit from the world class education on offer, irrespective of their social or financial circumstances.
The North London Collegiate School was founded in 1850 by Frances Mary Buss, a pioneer of women's education at a time when society held the view that a woman's place was firmly in the home; very few schools then took the education of women seriously.
Miss Buss founded the school with the express purpose of providing an unashamedly academic education for women, which would fully equip them for careers in the professions. The fruits of her labours soon became apparent. NLCS produced many of the first women graduates across a range of professions: dentistry, medicine, the civil service, science, academia and the arts.
Since its foundation North London Collegiate School has been committed to providing an accessible, affordable education for girls of ability. As early as 1910 local and national governments grants enabled the school to take non-feepayers, a mix which strengthened and enhanced the academic standards of the school. The Direct Grant and, latterly, the Assisted Places schemes have enabled the school to continue this policy.
Despite the withdrawal of the Direct Grant scheme in 1976 and the Assisted Places scheme in 1998, North London Collegiate remains committed to providing opportunity based on ability, regardless of financial means. A successful appeal launched in 2000 has now improved the funds we have for bursaries.
The difference between a Bursary and a Scholarship
Academic scholarship awards are based solely on the entrance examination results at 11+ and 16+, with awards made on academic merit irrespective of financial means. There are no special scholarship examinations nor do parents apply for a scholarship. The value of scholarships is up to 50% of fees and is valid until the end of a girl's education at NLCS.
A number of music scholarships are awarded at 11+ on the basis of merit. Girls must pass the entrance examination and a music audition conducted by the music department to qualify. In addition, music scholars may be eligible for a bursary. Parents who wish their daughter to be considered for a music scholarship must fill in an application form. For further information and to download an application form, please read the Music Scholarship section below.
Bursaries are related to the income and assets of the family. They are means tested and reviewed annually. Bursaries may also take into account academic merit. It is not unusual for a girl to be a recipient of both a scholarship and a bursary. The value of bursaries ranges from 10% of school fees to 100%. Pupils holding bursaries may also be given help with expenses such as school field trips.
How Bursaries and Scholarships are awarded
Scholarships and bursaries are given to girls aged 11 prior to entry into year 7 or to new entrants joining the sixth form.
In exceptional circumstances, bursaries may be available to help girls in Year 10 onwards, whose parents are experiencing financial hardship and cannot meet the cost of full school fees. These bursaries are means tested and are applicable until family circumstances improve or the girl finishes her current examination course.
Bursaries are subject to an annual review and may be amended according to changes in the family's circumstances. Bursaries are a percentage of school fees and revalued annually in line with rises in school fees.
Scholarships are not means tested and no special application is required. Parents need not supply any financial details, unless they are applying for a bursary. Since scholarships are awarded as a percentage of school fees, the sum awarded rises with any fee increase.
Girls may hold a scholarship combined with a bursary to the maximum value of 100% of school fees.
How do parents apply?
Enquiries about scholarships should be made to the Admissions Officer. All queries about bursaries should be directed to the school bursar.
NB - Applications for bursaries can only be made if your daughter is invited back for an interview following the examination.
Following success in the 11+ examination parents will receive a letter inviting them and their daughter to interview. Parents seeking a bursary must then apply before the interview date and complete a statement of income and fixed expenditure. The Bursar or Assistant Bursar then interviews parents to discuss their application and financial circumstances.
A committee of governors considers each case individually and in confidence. When the assessment process is complete, the Headmistress will write to parents offering a place and at the same time indicate whether an academic or music scholarship is to be awarded, or a bursary made available. Academic awards are made at the discretion of the Headmistress.