Why do people always assume that private schools have "ridiculous added on costs, trips, transport, lunches exorbitant uniform prices etc.".
Some might. Lots don't!
For example, DS' indie school, South London. Blazer is a bog standard black polyester one, cost £30. Any black trousers. Any white shirt. Badged (acrylic) jumper if you want to wear one. Polyester tie, about a fiver.
Admittedly the sports kit is extensive and relatively expensive, but no more so than the state grammar school that my nephews go to. And our PTA run second hand sales every term, so there's no need to buy anything new if you don't want to.
Any subject-based day trips that are required e.g. geography field trips, history trips etc, we are not charged any extra for. There are expensive residential trips, but none of these are compulsory, even if related to a subject, and plenty of boys don't go on them. My DS have never been on any of those (out of choice, not budget) and don't feel as though they've missed out.
All extra curricular clubs are free, other than music lessons. School lunches are not compulsory, you can bring in a packed lunch, and if you want to buy a lunch it's very reasonably priced. You don't have to pay for a whole term of lunches or anything, you just top up their lunch account when needed, via a parentpay-type account.
If you want to get the school minibus to school, it's no more expensive than taking the train every day.
About 40% of pupils at their school receive financial support, via bursaries or scholarships.
And they are certainly not "told they are better than everyone else" 
Please stop assuming every private school is like Eton or Winchester. Most aren't.