I think Hula's child is at a private primary, hence the larger selection... Just remembered we've also had Eco-club, gardening, sewing, recorder & choir club at our school in past (a few lunchtime, but most after 3pm). All ran by staff (overwhelmingly TAs with own DC at the same school). Most the clubs are free.
Yes Dd's is an independent primary. Not big though, about 100 girls. All staff run at least one club I think and the music ones are linked to music lessons and/or orchestra and choir that all of juniors are involved in.
We have 3 male staff (out of 11!). Both of my primary-age DC have male teachers this year. I reckon they deserve credit for getting specialists in to teach sport, getting all the teachers to join in the school Fun-Run, and having a Table Tennis match at Dinnertime with each man's class cheering (and the other male teacher acting as referee). Feel very lucky (esp., as a mother of 3 boys).
sunflower - an external company introduced it - did a taster session when ds was in reception - which he really enjoyed and wanted to do when he got into Yr1. Its run by Yogabugs. They do stories and weave the yoga poses in - but the movements are a lot quicker (more like wayballo, but with a story connecting the movements).
Our little chruch school offers; Fun club (crafts for KS1), art club. Football, karate, sports club. Cooking, choir, jewelry making. Also has externally run French and science club. Our PTA also offers bursuries for the children who's parents can't afford to pay for them.