You ask about teachers administering punishment to pupils not in their class. In many schools some teachers would have their belts with them in the corridors. When outside the classroom and on duty it was was usual for teachers to carry their belts held looped in one hand, or to have it slipped over their shoulder under their jacket.
Some teachers would be on “corridor patrol”. Their function was to supervise behaviour in the corridors when classes were changing rooms, or at break times or at the start and end of the school day. They would be on the lookout for offences such as “running in the corridor”, “going the wrong way up or down stairs”, pushing and shoving, excessive noise, rowdy behaviour etc. When they came across any such offences the pupil/s would be stopped, the belt produced, hands held up and the punishment administered on the spot, often in front of other pupils passing by.