In Britain, private and public schools are pretty much the same as each other. In America, they are different, as 'public' schools are the same as British state schools
how is soccer a british clue? and eraser? those are fundamentally not the things that are british. the answers, football and rubber are more suited for the 'british clue' column
Nice quiz idea, could be developed a bit? eg, what USA calls a trunk (of a car), Brits call a boot. A trunk is either a big suitcase or an elephant's nose