I spend roughly £100 per month for myself, DH (including packed lunches) & DS aged 21 months (huge appetite) - plus 1 cat.
My method is completely opposite to most of those on here - I rarely plan at all!
I go to my local tesco (lucky to have a big store 1 mile from my house) every once in a while at 8pm. I then buy meat, fish, pies etc at 25% of the original price & fruit & veg at 10% of the origianl price, as it is on that day's date & they have marked it down (eg the other day I got a whole load of prepacked fruit salads for 7p each, broccoli heads for no more than 10p each & packs of rosemary for 4p each). Once I get home, I divide everything up into meal-sized portions & freeze it. Fruit, I puree/stew & freeze. I rarely spend more than £20 a time doing this & it usually provides main components of 15-20 meals, if not more.
I supplement the above with weekly milk, yoghurt & bread runs (or walks, to be more accurate!) which are about £5 for all I need for the week. Things that cannot be bought reduced are usually value brand (& taste 90% as good, if not 100%).
I buy big boxes of washing powder when on offer & these last me 6 months or so - I use half the recommended amount & clothes come out fine. I only use bleach, limescale remover & tesco value all-purpose cleaning fluid (less than 50p a bottle) to clean with & find these adequate - I hate the idea of too many chemicals & some actually give me a headache or sore throat if I inhale the fumes. D/w tabs & fabric softener are value brand, nappies & wipes tesco own brand & bought when on special offer.
I see you have more DC than I do,OP, but I think your goal is perfectly attainable. Good luck with it 