And in any case wealth is not a consideration here. The school requires no payment from parents. There seems to be an unchallenged connection between wealth and good schools, almost as if either the parents' wealth improves the schools or the schools react to the parents' wealth.
This ain't necessarily so. Better off parents tend to be more well educated themselves and engender an atmosphere of support and encouragement around their children when it comes to education. (I am not saying this is exclusively so and without exception but in general). As a result their children tend to do better at school and the school itself performs well overall. It is not wealth which drives this but philosophy and behaviour.
It's a bit taboo to say so, but schools in "poor" areas tend to have a larger proportion of pupils whose parents do not provide such a high level of support and encouragement for their children's education and (very importantly) behaviour. A small number of disruptive pupils effectively slaughter any good work the school may put in. That's why, if State education is to suceed in the UK, selection by ability is absolutely essential.