The Guardian think so. Our food is labelled to show the physical impact it has on our body, so why should it not be labelled to show the environmental impact? I personally couldn't agree more with this article and I think it would make a real change to the way we buy food if we could see the impact it is having.
https://www.theguardian.com/environment/2018/oct/10/we-label-fridges-to-show-their-environmental-impact-why-not-food?CMP=share_btn_tw