I suppose if the number of Prime Ministers produced from Eton is anything to go by, then we could look at other public schools to check for number of PMs, if at all and then look to their sister schools, if any.
St Paul’s Boys’ School produced Spencer Compton as PM and George Osborne as Chancellor. There is St Paul’s Girls’ School so that could be seen as an equivalent to a girls’ Eton in some ways. It churns out many successful women.
Westminster produced Nick Clegg, girls are admitted in the sixth form.
Habs hasn’t produced any PMs.
City of London Boys’ had Herbert Asquith as Prime Minister and Earl of Oxford. There is a sister school.
Dulwich College has no PMs
Stowe has none.
Wycombe hasn’t produced any female PMs, although plenty of successes in other areas.
Cheltenham Ladies’ College and Roedean have traditionally been held in high esteem.
Then you could look at members of the Royal Family, Victoria Crosses awarded, QC appointments, etc.
The Public Schools Act of 1868 lists:
Eton, Harrow, Westminster, Winchester, Charterhouse and Rugby, with City of London School added at a later date.
St Paul’s and Merchant Taylor’s’ were excluded because they were deemed by the Clarendon Report to be ‘private’ rather than ‘public’ schools, so any abuse could not be legally challenged, unlike all the former which had been originally established as charitable schools.