My not-posh DC learnt to sail with the Scouts. £100 each for 4 days tuition, kit hire and sailing fur the rest of the season - we deliberately chose the course the first week of the summer holidays to maximise the rest if the season.
DD plays chess, plays in a club at school (state school). She loves the game. The club is supported by a maths teacher.
The DC's school used to run a ski trip, but havn't for the last few years due to CoL. DH and I were both super keen skiers hire we had dc, but it's been pretty cost restrictive since we had the second child. I'd love to ski again, and it is looking more like will we could afford it, although not sure about the reliability of snow anymore!
Rugby - we live in the home of Rugby League! Pretty much every child I know locally, from all walks of life has played rugby at some point. A few of ds's Y10/11 peers have got scholarships etc with the local professional club. But I suspect the purists will tell me that League is anything but posh.
Riding - I did a bit as a child, I was never that into it. DS has a friend who has ponies, has ridden all their life etc, but neither of my dc has ever expressed any interest.
DS has a friend who is learning to fly. Lifelong dream. Sounds posh, but he id waitering in a food pub at weekends to pay for lessons. He can afford about one lesson a month, his family can't afford to support this passion.