Private schools bursaries - a question

Does anyone know how, if at all, how the awarding of private schools's bursaries is monitored? On what basis are they typically given? To whom? What is the background of those getting bursaries. Are kids tested? How?

If you don't have general knowledge, you may know of particular instances of how bursaries were awarded.

My guess is, they are not really monitored at all. But as this is the main "public benefit" private schools provide for 100 million pounds of public money (in tax), shouldn't it be very closely monitored?

The only kid I know who received a bursary had a father who went to a top public school and a grandfather who is a Knight of The Realm. No academic selection. Just an interview to see if he would "fit in". Which he obviously did.

How many kids from council estates get bursaries, I wonder? Maybe the mechanisms for awarding bursaries are not as dodgy as they appear to me to be, but I'd like to be reassured!