We shop at Ocado and top up locally at Sainsbury. I never go over £100 on the online shop, more often between £70 and £90. I do have milk delivered and usually buy an extra carton at sainsbury each week.
I also tend to do a big shop at wilkinson once every 3 weeks-ish for dishwasher tabs, surface cleaner, cleaning sponges and so on.
With the main shop I have to include nappies for baby plus wipes, pull up things for bed wetting DS, a few cleaning/toiletries bits if I haven't stocked up at Wilko, cat food and then all the bits for packed lunch and breakfasts and evening meals plus snacks.
If I have to I can do the whole week on £40 but my store cupboard tends to get very low then.
What I describe above is for 4 children aged between 1 and 10 plus me, and about 3 meals for DP each week when he eats with me at my house.
I live on pitta bread and dips which really keeps cost down. DC can do lunches on £20 a week for all 3 school children (sandwich, fruit, crisps and yogurt plus a biscuit or flapjack. After that all we need is a few bits of veg, usually staples are carrots, potatoes, leeks, onions, and then whatever we fancy; then we get minced beef and a pack of mini chicken breast fillets or perhaps fish; buy tinned tomatoes, rice and pasta and pulses on the dried goods side of things and then a few dairy bits like mega packs of cheese and we are all sorted.
Our luxury items are the crisps, any chocolate bars for packed lunch, biscuits for after school and then I let them have chocolate mousses or ice cream as mid week deserts which we live without if necessary. I also buy me Pepsi max as is an addiction I have and the DC sqaush.
Hope that helps. I also think Asda and Tesco are a false economy and also if I actually go into either of these stores I get sucked into buying crap. For example (we went to Asda to buy Hallloween items this week) I bought chocolate spread, and some cakey carby bits that I never buy normally this week because we went into Asda and I was tempted.