Straight away I'd tell you it is where your shopping.
We shop at lidl for our main shop and we usually do a monthly shop(because it saves us a fortune but honestly it is mainly because I hate shopping,but it does save us a fortune)of all of the dried goods and things that can be frozen(we have a large fridge with a small freezer and a chest freezer)and then the fresh stuff is done weekly.
On a high spend month we'd spend £400 and that is for 8 of us(myself,DH,DS's 23,21 and 18,DD's 16 and 12) including our grandson and our 3 Dogs.
We eat really well for that,steak,salmon,fresh chicken breasts,steak mince,legs of lamb,whole large fresh chickens,joints of beef and pork,good quality sausages,gammon,bacon ect.
We buy some own brands but they're lidls own brands so much nicer tasting and much better quality than a usual supermarkets own brand.
Toiletries,some are supermarket brands others are name brands and I end up having to buy quite a few and different types(so 4 different for my 3 DS's and DH,a different type for each of my DD's and myself and then another different type for my DGrandson)2 different types of washing powder/liquid.
I know you said lidl is further away but the amount of money you'd save it would be well worth it even if you did 1 shop a month there for your dried goods and frozen bits and for the rest if you have an asda close by I've found them to be alot cheaper than sainsburys,tesco and morrisons.