Girls at my school could be smacked by the headmaster if bad enough.
However, they usually would be sent to the female deputy but for a serious deterrent.
This was only a first or maybe second-year punishment for most girls.
However, I do remember a few being sent to his office and returning red-faced and often in floods of tears.
The cane was rarely used on boys never mind girls at my school.
The older girls got the slipper off the deputy headmistress and the boys got the same from the headmaster.