Woodpigeon can be shot at any time, if you have the landowner's permission.
I've permission on arable land round me: what we call stoggies are a real pest in emerging crops in January and February, and in late summer.
The meat is a vital and delicious supplement to my larder, along with rabbit, pheasant, venison, partridge.
The feral pigeon is another beast altogether. Would not be on any menu of mine.
I'm also happy to cook roadkill if it's fresh.
Folk are massively disconnected from where food can be had. For every pigeon I shoot, there must be a hundred good meals getting away.