Where's the Beef (Tax)?

The UK Health Alliance on Climate Change (UKHACC) is a body incorporating 10 Royal Colleges of Medicine and Nursing, the British Medical Association as well as the Lancet journal. So it is pretty representative of the professionals that look after human health in this country. The UKHACC are advocating a climate tax on food (such as meat and dairy products) with a heavy environmental impact to be introduced by 2025 (https://www.theguardian.com/environment/2020/nov/04/uk-health-professions-call-for-climate-tax-on-meat). They obviously think that the tax would produce health benefits by both a) reducing the amount of meat and dairy products consumed and b) helping to pay for the impact of their production on climate change (cattle are big producers of methane). The taxes would presumably be levied on both UK-produced and imported foods? It seems a not unreasonable suggestion, so long as it doesn't fall only on the poorer sectors of society.