Rhubarb-if you were to move anywhere near Liverpool and had a DD this school may be of interest. The Sutton Trust pays full fees/contributes towards fees for girls from lower income families post-11 years.
otherwise most private schools offer scholarships/bursaries. Also schools supported by a particular group e.g. Haberdashers have hardship funds so that kids can stay in the school if the family loses their income.
BTW-we are ordinary and have a DD in private school. Really mixed bag of people, yes there are the 4x4s brigade but these are a minority. At DD's school I would guess that most people are actually first generation private school users. Also a lot of parents have their own businesses e.g.builders, electricians rather than stereotypical barristers and accountants.