On the other hand, as I’ve recently mentioned in another thread, “reasonable chastisement when acting in loco parentis” was a defence to a charge of ABH up to 2004. Profuse bleeding might be GBH (to which this was not a defence) but light bleeding might have been ABH and therefore not illegal.
As a matter of interest (though I can’t find the reference at the moment) at least one nineteenth-century schoolboy is known to have died as a result of injuries sustained from corporal punishment; I believe that the headmaster was convicted of manslaughter.