I don’t think that sounds as much as it looks, OP. We spend up to £500 a month for four of us (2 adults, 1 primary school child, 1 toddler, 1 cat). That includes all cleaning products, some packed lunches (not for DCs), quite a lot of snack foods but no alcohol, nappies for the toddler, some children’s toiletries, and cat food. Alcohol not included, nor is eating out/takeaways.
I try and mix it up between Aldi and Sainsbury’s deliveries - spent £85 at Aldi this week and I bet it would have been over £100 in Sainsbury’s. But the delivery factor wins out some weeks!
We have a fair amount of batch cooked meals, stuff like chilli, lasagne, goulash, etc.
I suspect you might be able to get that down a bit but probably not by more than £100 per month, depending on where you shop and how you eat.