@fendertele - in this household (just the two adults, with hearty appetites) we are fortunate to have a flexible budget for food, but I feel positive we don't spend as much as you do, on a day-to-day basis.
In terms of meat, we only buy from our local butcher, whose meat is excellent quality, and cheaper that supermarket meat.
Do you ever make a roast? We have a roast at least every Sunday, with an informal rotation of beef, pork and lamb (MrB isn't excessively keen on chicken). Curiously, we were discussing the average price of our Sunday Roast just this morning. Our boneless leg of pork joint for tomorrow was c£6, and will give us excellent crackling (calories++), plus cold cuts, probably on Tuesday. A beef roast (Salmon Cut) is about £8, with boneless leg of lamb usually £12-13.
Once you get to know your butcher, he/she will tell you of anything they have that's particularly good, plus any offers. When the butcher does offers, I'll often buy extra for the freezer.
Chickens, we we do have it, I always buy whole, so have the whole bird at our disposal - at least 4 portions, plus the carcass for stalk and carcass picking into soup.
Pork belly is delicious and nutrition dense. Cooked in a slab, it makes an excellent roast, or strips cut, the grilled or BBQed can be staggeringly good.
An omelette with diced chorizo, or bacon lardons, with added grated cooking cheese near the end, the melted unde the grill is very filling and again nutrient dense. Cooking cheese in Lidl is under £4 for 900gr. I grate the whole block at once, then freeze in 100gr portions, so that I am not prema welded to the grater.
I make my own yoghurt - 2ltrs at a time, using UHT milk (the process is just simpler with UHT), and starter from the previous batch. 2ltrs of UHT is under £2. It keeps very well in the fridge. It might seem a lot of faff to home make yoghurt, but the majority of the magic happens as we sleep.
There are a few albeit fairly aged threads on here about living low carb on low income. Could be worth a search. There could just be some helpful ideas on there.