I was frequently caned at my London grammar school in the mid 1960s and never had marks like that even after six strokes. The only marking was short thin red stripes across my arse made by the tip of the cane.
Canings were given across our ordinary trousers, we just had to bend over and lift up our blazer. Some teachers caned on the hand. Occasionally a boy might be slippered on his gym shorts during PE but I never heard of anyone being made to take his trousers down or change into PE kit for a caning.