We do a lot of the things mentioned on here. I'm vegan, so dirt cheap to feed: I buy sacks of pulses, grains, nuts and seeds in bulk (multicultural shops are the best for this), and own brand/value frozen veg. I buy plant milks in bulk when they're on offer. I make my own beanburgers.
For omnivore DH and DCs, I buy meat in bulk from MuscleFood every couple of months. I do a lot of batch cooking with this, and pad out mince dishes with lentils or soya mince (you can get big bags of this in its dry form, much cheaper than stuff like Quorn).
I buy big bags of porridge oats instead of breakfast cereals - much, much cheaper, you can add whatever you want to it, and make granola/muesli out of it too.
I make my own bread, tortilla wraps, pizza bases and sweet treats (flapjacks and brownies cut into small squares are always good). I bulk buy tinned tomatoes and passata and make my own sauces.
We also bulk buy dishwasher tablets, toilet roll and washing powder - Amazon is good for this, and sometimes cash and carry places have bargains.
The only things we buy in the week are ordinary milk, salad, fruit, and any other fresh ingredients we might need.
It's worked out a lot cheaper this way, but I admit it takes a LOT of forward planning! I have a strict meal plan, and I stick to it - it's not always fun, but I do my best with it. Food shopping is so bloody expensive.