Hasn't anyone thought that there may be a genetic influence here?
If people are rich, chances are it is because they are very clever. If not clever, then have some talent, like sport or music. Even if you don't agree that these people should be paid highly, the people who consume their services do, and it would be horrendous for the public sector to meddle in private sector wages (although this is another debate altogether).
Of all the very rich people in the world, not many don't deserve it. This is often passed down through their genes to their children and grandchildren, meaning they are also very intelligent people. Going to a private school simply enhances this natural intelligence, allowing them to use it to the full potential. Even if they didn't get the best education (except maybe if they were in one of the worst schools in the country), many of them would probably still make it into one of these top jobs. Surely it is better to try to move the standard of the worst off upwards rather than prevent those at the top from getting too far ahead of the others?
I don't understand why people are so against the private schools. People may see this as the 1% screwing everyone over again by getting a better education than us, but think of it in this way. These are the people who contribute by far the most to tax revenue, which pay for schools, hospitals, benefits and welfare etc. However, if they are privately educated and go to a private doctor, they use far far less in government resources than the average person, and the difference is even more astonishing when you consider how much more they provide to the public purse than the average person.