Conkers is about the least upper class game i can think of. We played it on council estates.

We used a corkscrew then threaded a shoelace through it.

I played conkers in the 80s, everybody in the school did. People had tricks like coating their conkers in gloss etc. but it was still a widespread game. Played football and British bulldog type stuff too but conkers came in season for a bit every year.