I too believe this legislation prohibits animals, which are generally defined as farmed animals (which includes chickens), from being fed waste from a kitchen or even food prepared in a kitchen which is also used to prepare human food. This is to prevent an animal, which might enter the human food chain, being fed any animal products (meat) or any feed which might be contaminated by an animal product. So it's OK to feed your pet cat or dog anything prepared in a kitchen but not your pet chicken even though it will never enter the human food chain. In a chicken's case the eggs will no doubt be entering the human food chain.
The legislation was brought in in the wake of the BSE problem, which was a big wake up event for British agriculture, and designed to prevent cross contamination between species which form part of the human food chain.
If you are doing this with vegatables but not meat products the chances of actually being prosecuted for doing it are remote. However if you were feeding your animals from the waste from your local takeaway that would definitely be breaking the law and could result in prosecution.
This also has implications for feeding chickens cat food a practice which I often see suggested as a way of adding protein to their diet during moult.
It's also no defence to leave such food available so the chickens have access to it and help themselves. If you take no precautions to preclude chickens from the dog or cats feed bowl you are technically breaking the law.
Whether you agree wiith this or not, or think it nonsense, is irrelevant in the eyes of the law, that's the way it is.
HF