Basically don't shell out on processed stuff that costs more, we very rarely eat any store bought cakes, biscuits, soups, ready meals, sandwich meats ice cream, sweets, chocolate, etc etc. Partly because those things are crazily expensive and partly because they are so unhealthy I would never feed them to my child on a regular basis anyway.
Also make use of the "reduced to clear" section. Figure out what times your local supermarket reduces produce right down to 5p and 10p. I have come out with a trolley full of meat, fish and vegetables for less than £5 before. If you are smart and buy stuff you can freeze then it never goes to waste.
Make use of the basics sections the products are half the price and 9 times out of ten are just as tasty.
Plan meals - always know exactly what you intend to cook for the week and buy only enough for that. For snacks buy value bags of apples and oranges. £1 a bag and you get about 10.
Keep the larder stocked with basics, pasta, rice, herbs, stock cubes, tinned tomatoes, salt and pepper, porridge oats and UHT milk. That way you always have a cheap and easy meal if your housekeeping budget is running low at the end of the month.
Use the budget supermarkets. Home Bargins near us is fantastic for dry goods like porridge, cereals, pet toys and treats, canned veg, tea, coffee, sugar, rice, etc, Aldi is great for cheaper cuts of meat and tinned fish, cheese and some vegetables - although choice can be a little limited. Also make use of the local farmers market if you have one, eggs, fruit and veg are often a lot cheaper than you would pay in the supermarkets.
Also use leftovers, vegetable peelings and meat trimmings make superb soups when combined with a little pearl barley or some lentils which are extremely cheap and good value. Boiled potatoes can be fried using a low cal oil spray or diced with some onion and a splash of ketchup or salad cream to make a potato salad which goes great in a packed lunch.
Honestly I don't do half that stuff at the minute due to lack of necessity forcing me to and lack of time to do so much shopping around - the month I tried doing it all as an experiment I spent an average of £17 per week for three of us. Two adults and one child. The budget for that would have been £397, which to me is an obscene amount to spend on food, I couldn't spend that if we were eating lobster and fillet steak every day unless I was buying a tonne of unhealthy processed rubbish.
