I know people will scoff and scoff as it has become such a cliche but the good old MN chicken is one of the cheapest ways. Buy the biggest chicken you can find for around £3. Yellow sticker is okay as you cook it all same day.
Roast it in a pan with one of the big potatoes cut into wedges and tossed in a bit of oil, and carrots. If you like, add garlic or herbs or lemon zest if you have some. Cook some peas or broccoli or cabbage.
Cut off the legs and divide into two thighs and two drumsticks, Slice two slices off each breast. Each person gets a drumstick or thigh and a slice of breast. If they want seconds, a wing and a smaller slice of breast.
Next day, strip the chicken - the rest of the breast and all the meat from underneath. Fry up a leek and some mushrooms with rice and the chunkiest bits of chicken. Add peas, herbs. Or add curry powder/spices, fried onion, peas etc. Or sweetcorn and smoky paprika etc. Risotto or biriyani or paella.
Boil the chicken carcass with a peeled carrot, bay leaf, half an onion, and the trimmed stalk of the broccoli for stock flavour. Remove the chicken carcass from the water, put back the onion and carrot and blend. Add barley, chopped veg, herbs and the smaller bits of chicken to make a chunky soup served with crusty bread. Or boil the carcass with a sliver of ginger and some soy, take it out and add fine egg noodles, sweet corn, chopped spring onions and finely shredded carrot etc to make chicken noodle soup.
That's main meals for 4 people for 3 nights, all for around £10 total including the veg.
Then I'd do Spanish omelette - fry onion, dice up the other big potato, a red pepper or chopped broccoli, some peas. Beat half a dozen eggs and pour over until base is cooked, then grate some cheese on top and stick under the grill. Serve with salad and bread.
Final night - pasta with tomato sauce - either from a jar if there are any on offer or fry an onion, add a ton or two of finely chopped tomatoes, pinch of herbs, garlic if you have it. Cook for a while. Add any fresh tomatoes that might be going sift - a dash of vinegar and teaspoonful of sugar enriches the sauce. Serve with grated cheese on top and broccoli or cauliflower or whatever green veg is in season. Or mash up the avocado with a bit of oil and/or lemon juice, to be the basis of a pasta sauce. DH and I do that often and we love it. I add lemon zest if you have a lemon, or chilli flakes, a few fresh chopped tomatoes if you have some (I bought a massive bag of cherry tomatoes from Sainsburys for 80p the other day)
Those two meals would cost about £8-10 max between them, so that is 5 main courses for 4 people for £20.
I'd keep breakfast simple - toast and jam or porridge or cereal. Maybe whizz up some milkshake with a ripe banana or two and a pint of milk. Or use up that pancake mix.
If you need to do lunches, you could use the leftover rice or pasta dishes to heat up in the microwave at work, as those recipes are all for 4 people, with fruit for desert. For a child's packed lunch maybe make chicken sandwiches one day, with fruit for pudding and carrot sticks. Then you'd need to buy some cheese or salami or similar for sandwiches on other days, unless they like taking pasta or rice salads.