I don't know whether once or twice a week is better, but the key to eating healthily and economically is meal planning and avoiding waste.
Our weekly shop, delivered yesterday, was £65 for 3 adults, and our meal plan is:
Pork chops and mustardy butter bean with veg.
Beef nachos
Lemony smoked salmon and spinach tagliatelle (to be fair the salmon was in the freezer left over from Christmas).
Aubergine and tomato satay curry
One pot garlic chicken and green beans
Chana masala with pomegranete raita
Super smoky bacon and tomato spaghetti.
Lunches are homemade soup (some veggies bought specifically e.g leek and potato, but also always use up any odds and ends from meal ingredients. Also I bought some cottage cheese and avos this week for a different lunch, plus there's always cheese/beans/eggs for "on toast" if anyone fancies that (fairly rare), or leftovers if we cooked too much dinner the day before.
Breakfasts are porridge (from oats) or greek yoghurt with fruit (fresh or frozen) or granola or eggs or peanut butter/marmite/honey on toast.
Snacks are apples/oranges/bananas and this week lychees as they were on special offer. We don't really buy or eat sweets/crisps/cakes etc.
Normally, including all toiletries and household stuff, I average around £80-100 each week when it's 4 adults, around £40-50 for 2 of us, and we eat very well indeed.