Well a little off topic but I remembered a funny story DF told me bout public/ private.
When he was 18 him and a mate were totally drunk rifling thru clothing bin. Police came along took them back to the police station, asked his mate what school did you go to, he replied B.... grammer, well they were so nice to him drove him home straight away.
Asked Df where he went which he repied B.... High (the local public school). They turned round to him yelled 'get in the cell punk' and locked him up for 4 hours. True story.

I do know too of jobs going to people that had private school background. If it comes down to 2 applicants the one that went to the better school will win out.