Yes I would guess pigeons or birds of some kind. However on our plot they seem to just eat the tendrils not the leaves or pods. They only started to attack peas a few years ago so it's probably learned behaviour. I cover my peas now.
I agree about needing the whole plot covered with green netting. Ours looks like a camp site with all the netting! Perhaps we should have guard posts to stop the vandals as well! It would end up looking like Stalag XIV!!