jane I think perhaps we are talking at cross purposes. The school that you attended was, as you say, set up for children who had experienced the death of a parent. In the past, schools set up by certain trade associations were, I believe, quite common, as were housing "villages" for retired people.
I don't believe mega-rich people are sending their children to the sort of school to which you refer. They are going to the very expensive schools which have fantastic facilities and where the vast majority of pupils come from very privileged backgrounds.
Despite the fact that these schools are in effect very successful businesses, they are still treated as charities. Many of them do not fulfil their obligation to form meaningful relationships with state schools. My view is that it is impossible to properly monitor this and it would make more sense to just abolish charitable status.
As another poster said, some small private schools are actually substantially inferior to state schools. These ineffective schools benefit neither their pupils nor the country. In such cases, the only people to benefit from the tax relief is the owners.
I went to a secondary modern school in Romford, a fairly "working class" area. Even though the general feeling at that time was that nothing much could be expected of 11+ failures, it was a happy, well managed school and we too were taught to show consideration to other people and to contribute to our own community as well as support overseas charities. I can't see why targets in state schools should prevent such values being promoted - though I agree the excessive concentration on targets is depressing.