I dont understand this obsession with snacks!
I would provide more filling meals - including more protein in form of lentils and pulses and more veg, and extra courses if needed (see below).
Work out when the kids are hungry.
If they are hoovering up snacks when they get home from school, for example, try bringing dinner/tea forward or provide something like own-brand cereal and milk, toast (preferably wholemeal)with jam/peanut butter, oatcakes and cheese, or something home-baked. Home-made pancakes are easy and cheap as well as being lower in sugar (plus no added preservatives etc) and you can bake a batch and put them in the freezer then defrost in a minute ot two. Same goes for home-made cereal bars, muffins etc.
If they are hungry aftee the evening meal start giving a pudding if you don"t already - could be yoghurt and fruit, (maybe frozen fruit), fruit crumble (again, cheap and quick to make and you can use cheaper fruit like apples or frozen fruit to keep cost down). Consider serving soup as a first course.before what you would normally serve as main course. Substitute in things like wholegrain rice, pasta etc which are more filling (and healthier) than white varieties.
If they are still hungry after evening meal, give them own-brand cereal and milk, maybe with fruit like banana or apple added in, or a mug of hot chocolate.
If you are on a tight budget, don't feel that you need to buy lots of soft fruit - most of their five-a-day can come from vegetables, pulses etc in meals. Fruit can be cheaper fruit like apples and bananas and can be part of meal rather than snacks to make them go further. Frozen fruit or fruit tinned in fruit juice are just as good nutritionally as fresh. Consider growing some soft fruit in your garden if you have space. Most soft fruit is very easy to grow and after the initial outlay the fruit works out very cheap. Rhubarb, blackcurrants and raspberries are all pretty reliable and easy to grow to eat fresh or to make into puddings/muffins etc. If there are places nearby to pick wild fruit such as brambles/blackberries, raspberries etc, these are great fresh and also good for freezing and for making things like crumble and muffins.
The odd snack/treat is fine. I buy one sweet treat a week for each of my DC - one likes Oreos and one likes Mentos. If they eat them all on the day of the shopping, that means they have to wait a week for more! I sometimes also buy a pack of nice biscuits (whatever is on special offer) and we have ice cream as a pudding on Friday. However, the focus in our house is on healthy, filling meals at mealtimes.
Please dont feel.judged. Food is so expensive but there are ways of changing what you buy to make your budget go further.