Re: $$$$$$$
hmmm first of all eton is a boy only school... both princes william and harry and like thousands of ex prime ministers and politicians and scientists and etc etc went there.
Sevenoaks is both boys and girls and is rated the no.1 independent school in the whole country... the education at these schools is beyond compare. about 25-30% all get into oxford, cambridge and ivy leagues.
Other good schools are (mixed and girls only ) :
wycombe abbey, badminton, cheltenham ladies college, st pauls girls school, westminster school, rugby, malvern. They all have similar fees for boarding and Its a good idea to apply to at least 7-8 schools are they are very selective.