A few frozen blueberries is much, much cheaper than keeping a steady flow of fresh ones in, though. When I've tried to cut my food budget down, fruit is one area I cut down on. But will usually get some apples in, a bag of frozen berries for the freezer (I get the wonky ones) and a few tins of fruit, whilst concentrating the 5 a day on cheap vegetables instead. Especially carrot, onion, cabbage, swede, and lots of frozen veg.
Otherwise carby foods are generally fairly cheap, but can be easy to over eat even on a fairly modest Budget (why obesity and poverty are correlated) so I wouldn't recommend replacing fats and proteins with carbs and you may still need to portion control these, but at least they cost pennies.
Protein is always my priority on a low budget diet. Some cheap frozen fish fillets, fish fingers, tinned fish, kippers are also a great option, I usually keep a bag of prawns in the freezer because just a handful of them in a fish pie or rice dish can make it feel so much more luxurious (the basics range cold water prawns, so they are small and not too expensive, also work well in a prawn cocktail or sandwich).
Otherwise cheaper cuts of chicken (I prefer chicken thigh meat to chicken breast anyway, and drumsticks, wings, etc. All taste great in a nice marinade or sauce). A little bit of bacon goes a long way, mince you can bulk out and the mince with higher fat content is usually pretty cheap. Even better if you can get meat with a reduced label! Mince especially freezes well. Sausages are also a great option, and even cheap hot dogs at a push (they are a bit salty but I make a hot dog jambalaya which is actually so nice!)
Otherwise beans and pulses are the best friend of every budget cook. I just wish my kids would eat them but that's another story! These are great for bulking out mince based meals, but increase the quantity slowly because as much as people will tell you you can't tell there's lentils in the cottage pie, or wherever, you really can if there is a lot in there. I add like a handful, alongside upping the veg content a little, which seems to work a lot better than subbing like 50% of the mince.
Eggs are also marvellous things. They can get expensive if you use a lot of them, but they can also be used more sparingly to increase how filling meals are, and are great as a binding agent in things like corn fritters, homemade burgers, fish cakes etc.
Baking is a good way to save money too, but it does depend a lot on what kind of things you bake and how you use the oven as well. I like to try and squeeze in a loaf cake of some kind whilst doing the roast dinner, but if I was running an empty oven to make a few cup cakes or making a passion fruit roulade every night, it might be cheaper to buy some supermarket cakes. Generally making your own Bread is pretty expensive when there is cheap store bought readily available, but you could save money making cornflake cakes (no oven needed) or dinner Rolls (in an already hot oven). With energy prices increasingly an issue, it is worth factoring that in. There are ways to reduce the cost of oven use, especially making the most of your microwave. Eg. With baked potatoes doing them in the microwave for the bulk of cooking time, then brushing with a little cooking oil and crisping up the skins in the oven. Potatoes are probably one of my favourite budget foods, all through for ideal nutrition eat the skins!
Freezer food is your friend on a budget (so long as you have a freezer and space!) it's cheaper to keep a full freezer cold than a half empty one, so make the use of every inch of space. Much Cheaper to keep chopped garlic, chilly, herbs etc. In there where it can't go off. I find onions don't work so well, and prefer to get them fresh for maximum taste. But they aren't terrible in a fix. Frozen veg, peas have a great protein content especially, but depending on room this is a great way to increase the quantity and variety of your veg consumption. Most foods are cheaper in their frozen state, but actually have better nutritional content than fresh items on a short date. I know things like fish fingers and breaded chicken get a bad rep, but it's a good protein source and often fish is omega 3 packed, breadcrumbs are sometimes wholegrain, and if baked not fried the fat content is minimal. If you don't like the breading, can always remove that too. But it's not the hill I would die on.
My favourite ingredient on a low budget is cheese, because even a tiny sprinkle of grated cheese makes most meals seem a lot more palatable and indulgent to me and you still need some dairy. Some cheap natural yogurt is a great way to get your dairy in too, and can be used to make dips, as an ingredient, or a nice dollop with a chilli. It's also great with porridge, if you make it with water can stir through a spoonful of yoghurt to make it nice and creamy (ideal with some grated apple, ginger, cinnamon and a few sultanas). Another great option is soured cream.
Meal planning is the big money saver, so that if your going to buy milk, you use all of it up. Same with yoghurt. Or salad greens. The biggest waster of these kinds of product is literal waste. Throwing food in the bin is the ultimate money waster, so being clever at making use of all of the product. There are lots of so called 'luxury' ingredients which you can eat very cheaply so long as you use them carefully