As I understand it, before the 1880s the birch was used in almost all schools. These were mainly Public Schools as the state school system as we know it was in its infancy.
Victorian prudery meant that another implement should be used and the cane was substituted because, unlike the birch, it was effective on a clothed bottom.
This presumably means that the 1880s/’90s were the heyday of caning but I would think the heyday of caning on the bare was the 1930s. The Victorian prudery had dwindled in the 1910/20s and to have an ‘ultimate deterrent’ the dreaded order became “Take down your trousers!” This gradually became the norm in public schools in the 1930s and was only quashed for good by the equalling of the classes in WW2.