Get your teens cooking, give them an amount of money to shop with and let them keep the change. Either have them do it solo or as a group - you know how they get on with each other. If you watch any of the masterchef series allow them a 'basic pantry' of things like salt and pepper, milk etc. If you don't then make the teens watch the US masterchef junior.
Have one meat free day. Until the 1980s I remember the phrase, "They eat meat everyday" meaning a family was quite well off.
Do you buy things like pizza? Easy to make at home for much less.
Also people who buy from the butchers, the butcher is more expensive than the supermarket
I find mine costs about the same but the quality is so much better. The shop is in the middle of a council estate and is always busy. He opens at 7am for businesses to buy so maybe that helps him stay competitive. He often knocks off the extra few pennies and if you go in for, say, 6 sausages and he has 8 left you will get the extra 2 for free. He also gives away 1kg bags of trimmings from the cooked meat - great for the cat.
Can you grow some veg? I have a pear tree that just sits in the garden and produces pears, I think it cost me £10.
I grow spring onions on the window sill. Basically get a bunch from the supermarket, cut off the 'bulb' bit at the bottom and stick in a jar / glass of water - they just regrow.
Don't just plan meals, but plan for the leftovers eg I do chicken in the slow cooker with creme fraiche and a tin of mushroom soup. I might add leeks and mushrooms to it.
I'm on my own so it is always too much but following day I put the leftovers in pie tins and top with pastry and freeze.
If I get a rotisserie chicken from the supermarket the following day the carcass is stripped of the meat for a curry (or frozen) and the carcass put in the slow cooker to make a stock which is then used to make French onion soup.
I'll echo what AlternativePerspective said about brands and home brands, supermarkets don't manufacture and often the same tin / packet / bag is sold with different labels. Eg Foxes used to (probably still do) make M and S biscuits.
Check out local, for want of a better word, 'ethnic' shops, I'm in Wolverhampton the many Indian and Pakistani shops have large bags of spices for 1/4 of what the supermarket charge. Coriander by the bunch and some amazing snacks.