There's a camp that seems like it does all the activities we'd expect from an American style camp:
https://campwilderness.co.uk/From the website:
"Days at camp are spent participating in a host of exciting activities, from traditional fire-lighting and shelter-building, to archery and wild swimming. And with evenings spent enjoying big bushtucker feasts, playing football and rounders in the fields, and roasting marshmallows over the campfire, Camp Wilderness is the perfect place to make great friends and long-lasting memories."
My boy went there last week and seemed to like it. He certainly came back absolutely filthy and had a hard time saying good bye to a certain little girl.
Still, I didn't get the impression that there was a big camp culture, with nicknames and songs and stuff.
We picked him up from one camp on Friday, then he was off to a different one on Saturday for another week.