Unfortunately we don't have CSAs in the UK. However there are farmers markets and some housing estates have their own veg growing cooperative where they then sell very cheap fruit and veg boxes/bags from what they have grown. I have five kids and our weekly shop averages at £65 a week usually from Sainsbury's. There is a lot of variety of frozen veg these days. Tinned veg is also fine but I try to avoid having it every day as some cans are lined with BPA. We try to avoid eating too much fruit, not only is it expensive but many fruits have a high glycaemic load meaning they give you a sugar rush then you crash afterwards. This is what I buy every week in terms of fruit and veg
18 loose bananas, 2 bags of apples, 2 bags of oranges or satsumas, 1 bag of kiwi fruits, 1 bag of potatoes, 1 bag of sweet potatoes, 1 bag of onions (though this lasts several weeks usually), 1 bag of mixed peppers, 2 bags of avocados, 2 packs of cherry tomatoes, 2 bags of salad, 2 cucumbers, some chillies, moxed bag of lemon and limes. Where possible they are from the Basics range.
Also every couple of weeks we buy a bag of frozen veg, the type of which we rotate. For example one time I but the basics frozen mixed veg, the next time Brocolli and Cauliflower mix, the next time spinach etc etc. Our freezer is now nice and full of a good variety of veg. I also buy tinned tomatoes, sweet corn, chickpeas and kidney beans. Lentils I buy dried and cook from scratch. Xx
ETA: we used to spend £120 a week 10 years ago when it was just us and food prices were a lot less. I don't even need to strictly meal plan anymore as we have a good store cupboard 'stash' of food to base meals on so even if I don't plan and then forget to buy something I really needed this week then I find something to sub it with and wait until next week