If you aren't wasting food, I would say it doesn't matter if you go more often, because everything will get eaten, plus you need to buy a lot, so it's going to cost a lot, and it might be more practical than doing infrequent massive shops.
So you need to look at what you buy, and get it for the best price, plus think of a selection of cheap meals that everyone will eat and shop for those and just cut some of the expensive meals from your repertoire. Plus look for offers and reduced items and make your meals around those.
For example, the range that something like a roast costs can vary massively. You might spend £20/30+ on a leg of lamb or beef rib or you could do a roast with a large chicken or a pork joint for maybe £10 or under. Serve a bit less meat and more veg, roast potatoes, Yorkshire puddings and stuffing to make the meal sufficient. With a large chicken, take all the meat off and it should be plenty for six portions. For veg, you could spend quite a lot on sprouting broccoli and a prepared root vegetable selection or you could get a couple of standard broccoli heads and carrots instead. You get the idea. Also look for reduced or special offer joints for the freezer, or see if there are any butchers doing meat packs you can freeze.
Likewise a chilli, put lots of beans and peppers in and less meat per portion.
I remember a poster on here who claimed it cost £28 to make fish pie because they bought their fish fresh from the Waitrose counter. You could reduce the cost by 70/80% by buying frozen fish from a cheaper supermarket instead (let the fish defrost, squeeze out the water and just put it in raw, add some veg like frozen green beans and cover with parsley/white sauce).
Also look at Costco but bear in mind that it's not always cheaper than supermarket special offers or buying in Lidl/Aldi.
For packed lunches, egg sandwiches or maybe cheese if you get big blocks of cheese at a cheaper cost per kilo or pasta salad with tuna in costs less than sliced meat.
Careful about the amount of drinks and snacks you buy, especially if your family use them up fast 'because they're there'.
For fruit, bananas and whatever is on offer, along with frozen berries, work out much cheaper than fresh berries or exotic fruit.