Unfortunately that's how our western culture/diet has matured, a propensity for cheap carbs and cheap poor quality proteins. Protein doesn't have to be expensive, but it's often cheaper to bulk buy. I.e. buy a whole chicken and roast it, rather than lots of chicken breasts. Fish is good, oily fish is even better, lots of calories, omega 3 good fats and protein.
However in general £ for £ you get more carb for your money than protein.
Buy from online butchers, you can get a meat box which can last a whole week or two (if you freeze it).
Most of our meals are protein based with stacks of veg. You just have to get used to changing your lifestyle to fit it.