Has it occurred to ANYONE, that parents who can afford to pay for private prep schools, are usually well educated themselves (that's how they got the jobs that pay well enough for the private school fees). They are intelligent, and intelligence is a very heritable trait. So their children will (usually) be intelligent themselves, and therefore more likely to pass the 11+, which is (essentially) an intelligence test.
Along with them, passing that 11+, are the children from state education who are equally bright and well read.
To make it totally, equally fair, I'd be happier if the 11+ consisted of the Non-verbal reasoning test, plus a Maths paper, comprehension and a sample of writing. Then you're not discriminating based on how widely read one child is over another. Access to books with complex language, along with access to adults willing and able to help you understand the words used, isn't fair across the board, especially for children whose parents are not well educated themselves. The local library may contain those books, but someone needs to encourage the child to read them, and help them with new words.