I used to buy whole roasted chicken for my neighbours dog when I was dog sitting for them. Last thing in the evening, go to the hot deli counter in the supermarket and see what is about. Often (this was Waitrose) they would be asking me to take the chicken for 50p or similar.
Also Waitrose tend to do 'ends' at the cold deli counter. You have to ask for them, but you or the dog could easily have any quantity you wanted for very little cost. I would often pick up 200g or so for under a £1. I would just clear out what they had available (he was a fully grown irish wolf hound - they don't come small!) I think they sold it at something like 49p per 100g. He often had pork, tongue, roasted ham, some of the really expensive stuff as well. Some stores don't do this and you have to ask over the counter for it. If you get a blank look, you know they don't. I suspect a standard butchers shop would also do it as well. The way to know is to watch when they are slicing the very end of the joint. If they put the last 2cm aside, then they probably sell them as 'ends'. If they continue to slice it, they don't.