Op you haven't specified specifically what the fussy eaters requires so it's hard to properly advise, but we also had a food bill that was getting out of hand. The good news is that when it's this high, some relatively simple cuts can make a big difference while still allowing you to not compromise in certain places. Here are some of the things I am doing. We were getting to about £900 -£1000 per month and am now down to about £700 without anyone really noticing the difference.
1 really look out for deals when it's on things you really have eg baked beans, mest, cereal etc and stock up what you can. Also cleaning products, dishwasher tabs etc
2 meal plan so that there's no waste and you can take a consolidated view. I try to ensure at least 2-3 meals a week are super cheap
3 as part of meal planning, what options to stretch are there? I bulk out bolognaise with extra veg and lentils, add chopped chorizo to v basic meals to make them more appealing (eg bean stew type things), use less meat in a stir fry etc.
4 shop online so you can properly compare prices. It can be much more difficult in store. We do buy in a certain amount of juice/drinks but I buy the brand or size pack that's cheapest each week. Eggs are another example - I was surprised recently to see that free range eggs even at waitrose can vary in price hugely depending on the brand.
Depending on your veggie flexibility, ditto. Seasonality and availability do make a difference in price. Eg I always buy cabbage but what cabbage changes every week.
5 as a die hard lurpak girl, I have been very pleased to discover that the Lidl dupe really is basically identical and a LOT cheaper. Lidl is also my go-to for decent quality and priced olive oil, pork schnitzel, peanut butter (without sugar or palm oil), granola and sauvignon blanc! 😆
5 I hear you that you don't like "beige" food for the freezer but there are some decent options that will be much cheaper than ready meals. Eg I buy fishcakes (often on deals) or crumbed/battered fish fillets or we buy waitrose chicken crumbed steaks in bulk as a much nicer version of nuggets that are relatively inexpensive and good for when ds and dh want an easy meal or need a more substantial snack.
6 pet food - I keep an eye on pets at-home website and get ours when they do deals. Dcat has just had food for the next 3 months delivered at a 20% saving.