Djinn, I've had two injured wood pidgeons in my garden.

In fact, one was so sick, that I put it in a big open top plastic box, watered and fed it and cared for it until the RSPCA center down the road would take him.

Poor thing. That was a couple of years back now.

As for cats, we used to get loads, but now we've stuck something on the tops of the fences which stops most of them from getting in. There was a cat sleeping under one of the trees the other day, though. It was only a tiny thing, so I was going to feed it some of the canned tuna we had at the time, but he got frightened and ran off when I opened the door to place the tuna outside.