I spent my early secondary school in some pretty basic and not-great state schools, but then got the opportunity to go to private school from the age of 14 to do my O-levels and A-levels. My parents were not rich, but I got an 'assisted place' where they didn't have to pay anything
The three big factors which made a difference for me were:
- Quality of teachers, which were generally very good.
- Class sizes. I had a class of around 20 for my O-levels, and 8 (yes eight) for my A-levels
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That's pretty much personal tuition.
- Definitely the confidence thing. When you are told regularly that you are the 'best of the best' then some of that rubs off.
I would disagree with the idea that all privately educated people use their connections to get ahead though. I never kept in touch with any of my school friends or used any connections, but still have done very well for myself (despite getting great A-levels and then deciding not to go to Uni anyway - much to my parent's horror).
So, can it make a difference? Yes. Do you need it in order to succeed? No (My kids have all gone to state schools and have all got exam results on a par with the best privately educated children).