What?
Public (Britain)
Private (Britain)
You've given Britain the same bloody option, for public is private here.
What you want to say is this:
Public (Britain)
State (Britain)
Quite correct terminology.
Public schools are owned and ran by private individuals, members of the public if you will, instead of being for the public like in the USA. Paying individuals can go to these schools.
State schools are run by the state, and are the ones that are free for the public.
Please make the necessary amendments, because otherwise only Public-schooled Brits can vote in this poll.
For the record, I am state-schooled, though it's supposed to be one of the best in the country.