The damning phrase “educational apartheid” has often been used to describe England’s postwar divide between state schools, particularly comprehensives, and their private sector rivals.

But for Peter Roberts, headmaster of Bradfield College in Berkshire, the divisions are all too apparent across and within both sectors, with one set of customs and privileges for the highly selective public schools and grammars (those that dominate our Top 1,000 ranking) and another for those with less of an academically selective intake, both state-funded and independent.