We are a family of 4 - me, DH, DS1 (3.8) & DS2 (16 months) & 1 DCat, and I spend anywhere from £100-£200 per month, so £25-£50 per week, on everything (including nappies for DS2, cleaning stuff, toiletries), depending on what stores we have in already. This includes all meals except breakfast, lunch & dinner for DS1 2 days per week, which will change in a couple of weeks.
I keep costs so low using a few different tactics:
Never buy meat/bread/bakery goods eg cakes, croissant/fruit & veg at full price unless unavoidable. I go to Tesco once every 3/4 weeks at around 7pm, kids in tow, and buy reduced items (75% off of original price) when they are marked down. These go straight in the freezer (we have 2) & means that the meat part of our meal is rarely more than £1 & I never pay more than about 40p for branded bread eg Hovis.
We make use of our local farm shops & farms. I buy a 25kg sack of potatoes for about £7 & store these in the garage, they last about 3 months. For the first time this year I also bought half a lamb from a farmer, this was £45 for about 20 meals, if you include heart etc - and I have the added bonus of knowing these goods are fresh & local & the kids love the visit to the farms 
I buy Value everything!
I get loads of freebies by signing up to test products on various different websites. In the last 6 months I have had at least 4 packs of nappies, 4 lots of laundry detergent, 3 lots of cat food, 1 full bottle of cleaning spray & 1 full bottle of Ambre Solaire suncream and more besides! All I have to do is fill in a short survey with my opinion of the product.
If I see a bargain grocery-wise, I buy it! So when a local store had tubs of Utterly Butterly on its date for 20p, I bought 3 & froze 2, saving a fair bit of money - most stuff can be frozen!
I forage a little. We are lucky enough to have a public park with an orchard on our doorstep, where we can pick plums, apples, blackberries, sloe & elderberries. The DC love to go & help me pick fruit for jam/stewing & freezing.
I would say we eat well. Today's menu is B - cornflakes (Sainsbury's Basics, about 30p/pack), L - sandwiches with yellow label naice ham, hm banana cake, avocado, raisins, value choc biscuit bar, D - lamb casserole (lamb 88p, carrots - 1 kg for 10p, so about 1p worth used, ditto parnsip & swede, 1 onion say 10p if that), which will feed me & DH, DS1 tomorrow & DS2 for 2 meals & jackets. We don't really have alcohol except what we make with our foraged fruits & biscuits/crisps are value & bought about twice a month.
I used to shop this way out of necessity & while I still couldn't afford to spend £100/week on groceries, I could spend more than I do, but I prefer to pay off credit cards with the spare money or go on a nicer holiday than I could otherwise do 