I went to a prep school where corporal punishment was just the perogative of the headmaster and his deputy.
At the public school I attended in the 1970s (one of those that ringed London) apart from the headmaster, the housemasters and their deputies, the PE master (unofficially I suspect) the prefects were also still allowed to cane. However, I think by then it was extremely unlikely that a prefect in a day house would do so and it never happened during the two miserable years I was in that school. As I understand it, the rules meant that any prefect beating had to be witnessed by six prefects. Sounds worse than a housemaster’s beating!
In reality the “normal” punishment was lines of the written variety!