Over here you generally don't here about anyone coming through state school cricket, since there virtually isn't any. Even though most of the county players are educated in the state sector, they play most of their cricket for clubs and the county/representative youth sides.
You can however trace the performances of up-and-coming young players in the public sector, through both the press (The Times runs a short report in the summer about schools cricket) and in Wisden. I can look back at Wisden's from 2001 and see young players making standout performances - hitting double-tons and the like. Alistair Cook was certainly well known for a number of years, even before he made his Essex debut.
With regards to individual schools, there are so many that it is difficult to pinpoint any main cricketing centres. Most of the coaching beyond the basics is done under the eyes of county coaches anyway. There is perhaps a circuit of between five and ten 'famous' cricketing schools (Eton, Harrow, Shrewsbury, Oundle), but they are by no means the best, just prestigious, ultra-traditional schools. When I went to play football at Shrewsbury School this year, they had a specialist indoor cricket school complete with artificial grass, six lanes of nets and full run-ups for the bowlers (obviously built following a donation from a wealthy ex-pupil). These schools play traditional, old-fashioned cricket, almost always declaration games, sometimes over two days (although saying that, Oundle experimented with 50-over games in coloured clothing, with a white ball and black sighrscreens). There are also so many schools that any talent is diluted out.
Brighton College does however appear to be producing some decent players for Sussex, both men and women, partly because of Claire Connor's work there. There are also specialist sports schools, such as Millfield, who basically only offer places to sportsmen and women up and around the international level. They can put out teams strong enough to play county academy sides, and regularly beat them.