I'm one of those people with a low grocery spend. First of all, a lot depends on where you live. When I see the grocery list Tass posted, I know I can get a lot of those things for much cheaper around here. Someone else might live somewhere where things are even more expensive. Second, portions vary. I have an office job, so even though I cycle to work and train with weights twice a week, I don't need a lot of calories. I used to have a roommate who was into body building and the amounts of food he ate were incredible. His diet also included lots of animal protein, which is expensive. He would easily go through a gallon of milk and two dozen eggs a week and would also consume large amounts of expensive protein powders. He ate a lot of expensive cuts of meat that are high in protein and low in fat. He chose more expensive fruits like bananas and avocado, instead of cheaper fruits like apples. Certain dietary choices really impact the food budget. Third, my partner often gets to eat at his work place, that's a perk of the job.
What makes a big difference for us, is that we choose to only use our grocery budget (in our joint checking account) for actual food. Not for snacks. When we go to the store together to get groceries, we pay from the grocery budget. When my partner buys expensive craft beers, or I buy chocolate, we pay from our own accounts. It really helps us to make that distinction between essentials and luxuries. We don't just throw snacks into our cart at the store, we consciously make the decision to go to the store to buy a snack and pay them from our personal accounts. Very often, we're not even bothered to go outside when we feel like snacking, thus avoiding that cost completely.
For breakfast, I eat basic oatmeal (0,40/pound) with water when I'm at work, with milk when we have it, and a piece of fruit. my partner eats cheap yoghurt (0,60/liter) with basic muesli (2,00/kg). For lunch, I often eat two fried eggs (0,25/each) with fruit or vegetables or leftovers from last night's dinner while my partner has another bowl of muesli (he really love that stuff) or simple bread (1/loaf) with peanut butter which in our country is normally just ground nuts with no additives (1,80/jar). For dinner we love simple things like potatoes / seasonal vegetables / meat stew (traditional dish from cheap cut of meat) or potatoes / seasonal vegetables / alternative for meat , vegetarian nasi goreng, vegetarian curry, chili con or sin carne or pasta dishes with a vegetable-based sauce. When we crave fast food we make homemade pizza or homemade fries. I try to can certain seasonal items as well.
As you can see, we eat little meat, we eat few snacks, we eat filling and cheap dishes. As you can see, our evening meal is normally carb-heavy but we also eat a lot of fruit and vegetables. We don't eat a lot of animal proteins, but we believe we get enough protein through other sources. We drink coffee once a day, otherwise we drink tea.
On top of that, we buy staples in bulk. The olive oil we buy costs 2,60/0,5 liter glass bottle, but the same brand is also available in 5 liter cans that cost 10,00. We buy a can, store it in the pantry and refill our 0,5 liter bottle 20 times from one can. I buy 5 kgs of apples or pears for 5 when they're in season and can them to use later when they're more expensive. I buy rice, potatoes and onions in large quantities and keep them in the pantry. We often buy meat and bread when they're marked down because they will be tossed out the next day, then freeze them. We don't waste leftovers. We don't use paper towels, but regular old fashioned dish cloths. We buy 5-kg boxes of washing powder for 10 and use half of the recommended amount, without noticing any difference. A small box of washing powder from the same brand costs 5/1 kg. I use regular cheap vinegar (0,30/liter) as a fabric softener.
We feel happy with this way of eating, we have been eating like this since our student days, we don't do it to save on money but because we genuinely like it. I can imagine this doesn't fit your diet, but this is how we keep a low grocery budget.