It is assumed that Eton used ONLY the birch until it was abolished. This is not so. The birch was the ceremonial punishment by the head master or lower master. All other CP at Eton in modern times (by housemasters and senior boys) was by cane. I haven’t discovered how far back this goes in history, but certainly the very early 20th century, very possibly earlier.
(That piece in the Wikipedia article on Eton is mostly by me, except for the bit about Sebastian Doggett receiving the last caning, in 1983, which remains unconfirmed so far, though the date sounds about right.)