St Paul's School was, according to Christorpher Hibbert, founded in 1509 by the Dean of St Paul's Cathedral. It was at that time the largest school in the country. It had all of 153 students.
It continues its tradition of egalitarianism. It opened its first building in Hammersmith in 1884, and the school moved south of the river to Barnes in 1968. Famous pupils include John Milton, Samuel Pepys, Field-Marshal Montgomery and G K Chesterton. These are healthily outnumbered by pupils who are not famous in any way.
The little second-hand experience I have of it suggests that it was in the late 1980s a great introduction to the rave scene.