Camp isn't such a big thing in the UK, but I did go to one camp as a kid. And there were pay phones. And there were no limits whatsoever on using them to call anyone you chose to call. And there were no logistical problems with it either. I just recall us hanging around waiting for a phone to be free in the evenings, chatting and eating candy and larking around as we did so. It was no chaotic big deal, just kids hanging out while they waited turns. And there was more that a hundred kids there. And no cell phones in those days either!
I've never been to overnight camp, except "Outdoor School", which is a lot different. You go to that as a class, and share a cabin with 4-5 classmates, so the "stranger" effect isn't really there, except for the cabin counselor.