When I was at boarding school, we were sent back at the start of term with some tuck, which lasted as long as you made it last (or until it went bad… some years later, I still have my tuck box and it still has a lingering odour of rotten apple from the one occasion when I decided to take back something healthy). There was a tuck shop, but we were only allowed to visit it once a week and our access to our pocket money was limited too. You had to hand it in to your head of year at the start of term, and then sign it out like a bank account. If your head of year thought you were taking out too much money, they would question you etc.
We weren’t allowed into town for at least the first year, can’t really remember, and for the first five years we were only allowed into town at weekends, and even then only in groups of three or more. But we were adequately fed, three meals a day plus a snack at teatime, and somehow we managed to survive without stuffing our faces all the time. Constant eating would, I think, have been rather looked down on.
This was a British boarding school (obviously!) which, per discussion with peers at other schools, was apparently fairly typical for its time, and things don’t seem to have changed much either.