Scholarships are basically a marketing tool in many schools. They attract people to apply and when they have 2 offers or more, a scholarship can encourage parents/child to opt for the school giving the scholarship, even if it isn't the best offer.....not just because of the money saving (because many are token amounts of about £1k - helpful, but not going to make or break the decision for most when fees are over £15k for a day place) but also the sense of prestige that some parents (esp prep school parents) gain from telling everyone that Jonny got a scholarship.
Yes, some of the scholars will turn out to be very bright, but some also turn up in the lower sets or are lazy. Prep school students are more likely to apply for scholarships, encouraged by the school (which gains prestige and uses the no of awards as a marketing tool at 4+ and 7+) and also because the Prep schools are more aware of the requirements and can do the work witH them to get them ready - so music departments run theory classes and art departments run sessions to create portfolios or for art appreciation.
When schools are deciding who to give scholarships to, they of course look at who is most able in the differential areas as far as it is poss to tell) but other factors determine decisions too - so what other schools they have applied to, which school they are from and how many scholarships that prep school 'needs' to receive to maintain the strong relationship between them. It's a complex situationn with many factors feeding into who does and doesn't get the scholarships - especially with the arts based ones.
Most academic scholarships are based purely on entrance exam, so all have a chance regardless of the type of school they are from.....no extra application is usually required. However, as the pp said, more go to those who have been highly prepped, either by school or tutors or parents, because despite the best efforts of schools to make the exams untutorable, you still can give yourself or your child a better chance through prep in advance. It may not be possible to 'polish a turd' as the expression goes, but it is certainly possible to make a moderately shiny one even more shiny!
In my view, whilst Prep schools do help their kids to was the exam etc and certainly can make a big difference for non academic scholarships, a state school child who has a tutor or a switched on parent who is able and willing to put in the time and effort in prepping, can do as well in the exams themselves. Parent preparers always are more invested in the outcomes of their own child than a school, but the commitment, effort needed and conflict it can cause between many children and their parents means it's certainly not for everyone.
Good luck everyone. Hope they get their offers first of all and scholarships as a lovely bonus!