I sympathise. We can't seem to keep th eshopping down below this either - similar sort of family make up and the need to do three meals a day for everyone basically.
Have you tried Amazon Fresh? It has a lot of Morrisons/Booths/Iceland products and I do find that it can be cheaper sometimes.
We do quite a few meals with meat, but where the meat is quite stingy. Pasta sauces are great for this - eg I'll had half or maybe 2/3 of a chorizo ring to a tomato and vegetable based sauce for flavour and to satisfy the carnivores. Or I can turn a pack of sausages into a meal for all of us by takjing the sausages out of their skin and sort of roughly chopping then turning into a creamy sauce. Ditto chicken or bacon. These sort of things work well with Gnocchi too.
Another thing I do quite often is a pork mince sort of stir fry. So one pack of mince and then massive portions of veggies that I stir fry in batches until it's all done, with th emince, flavoured with soy and lime juice (plus garlic, chilli, ginger) and then serve with noodles. Works well when DS has friends over unexpectedly as i can just up the veggies and/or noodles without requiring additional mince.
I can't manage the MN single roast chicken to feed everyone for a week! But I do find it works well with enough leftovers usually to do a chicken salad with garlic bread or a risotto topped with chicken, and often then also to make some chicken sandwiches for lunch. So again, things that need less meat. Risotto generally is a good option and a good cheap version which, if you want to add meat, can be done in smaller amounts. I haven't done it for a while but I used to do a lemon risotto and then top with a little crispy bacon or even some parma ham (when it didn't break the bank for parma ham!). I might revisit that one soon for variety.
Chicken thighs are also good - often very reasonably priced and I slow cook them in the oven (marinade with a bit of oil, lemon juice, fennel, garlic, cumin and cinnamon, salt well then cook at 150 fan for 45 minutes, baste, then back in the oven for about 25 minutes). I serve this usually with new potatoes or mash and steamed veg. I usually make extra and use as I would leftover roast chicken.
I'm trying to do breakfast for dinner once a week or so - something a bit more simple and cheap. Shakshuksa for example. Or scrambled egg, with avocado on bread or whatever.
Snacks are a never-ending source of frustration here too. DS loves home cooked food but for snacks - he just wants convenience. Drives me mad. So we land up with fancy Kind bars when I can make snack bars at a much more reasonable price, but that's not hwat he likes. I do make an effort often to make a nice sandwich at lunch and then he has that as a snack when he comes in - toasted. If I'm organised enough I might do something similar with a wrap which he then puts in the airfryer (next step is to get him to do this himself). When he was younger I'd sometimes do him a jacket potato in the microwave and air fryer so that it was substantial and he could have it before going out again for sport. he does also often cook himself eggs or I'll boil eggs and leave them for him. We eat a lot of popcorn too!
He also does things like fish fingers or crumbed chicken breasts in the airfryer on bread/roll (Waitrose does good "frozen chicken steaks" which I think are about £2.30 for 4 and they're quite good quality and I don't mind him having one of those coming home from school).
Oh, and breakfast is mostly weetabix or shred dies, or scrambled eggs on toast or waffles/pancakes which are very cheap and much better quality than shop bought. I buy an 85p bag of flour about once a week, plus eggs and some milk and that's DD's breakfast everyday plus some days for DH and also something I put in her lunchbox.