There are a lot of parents on here who are quick to judge that stealing treats must mean the children are hungry, and the OP is somehow to blame for underfeeding them.
What nonsense. The children almost certainly had other, cheaper choices at their disposal that they wouldn’t have needed to hide to eat. They chose family treat stash over the bread, cereal, milk & spreads that, at their ages, they are able to manage, because they wanted the sweet & salty treats, not because they were being nutritionally neglected by their parents.
it is unfortunate that supermarkets have chosen to label crisps, cheese strings, fruit leathers & strings sweets, chocolate, biscuits & sweet bars of all kinds, as ‘snack’ foods. Parents are often under pressure from their children, and for the sake of convenience, to buy them. Such foods are treats & sometimes, conveniences, but they are expensive and not necessary to anyone’s diet. While I think Christmas is several months away, and the OP’s no-doubt frustrated initial decision about Christmas money might bear reconsideration, it sounds as though the family food budget is carefully managed, and the OP is reasonable to be worried about prices as well as sensible in understanding that children must be taught that actions have consequences.
I’d definitely deprive them of their usual treats for the month, but in terms of family budgeting, I’d also quietly reduce the number of ready-snacks (things that used to be called treats, because they were eaten once per week and often bought with the children’s own pocket-money) purchased each month, but the cereal & energy bars only for your husband, and spend some
of the difference on low-sugar breakfast cereals, bread, ‘sandwich vegetables’ and spreads. Crisps & so-called snack bars belong in the ‘treats’ rather than ‘snacks’ category for everyone except the manually-labouring husband, who does need regular energy top-ups to do his job.
Children don’t need more than two NHS-described servings of fruit per day (especially given that fruit between meals means that there will be sugar and fruit acids sitting on their teeth between brushings) so you might consider offering one serving as their lunchbox snack and the other as a starter or end to their evening meal.
Consider trying this. When they come home from school or a weekend sporting event, they will be hungry. Let them make their own after-school snack (teach them about portion sizes and specify, for example, the number of slices of bread or cheese allowed, and provide an appropriately-sized cup for cereal to be measured). Insist that they use a plate (and cutlery as well if appropriate), pour a glass of water or make a up of decaffeinated tea, put all screens & distractions away, and eat it as a proper meal. If preferred, this could be the time to allow the second serving of fruit. Give it a name: afternoon tea would be appropriate.
Set a timer for the meal (15 minutes for a sandwich or cereal) and do not let them go off to play or turn on a screen until the timer is up. They might wash their utensils and hands, ensure they have cleaned up after themselves, and allow them to sit and read or chat if the time isn’t up when they have finished, but don’t give them any activity options that might make them inclined to bolt down their food to get to it.
Children don’t need snacks after eating a well-balanced dinner/supper containing sufficient complex carbohydrates, protein & vegetables. They need a low-level family activity (telly, a board game, cards, or just a bit of free time) and then a bath, a story (they are not too old: it’s a great opportunity to introduce them to topics & themes that you wouldn’t want them to encounter for the first time on their own) and bed.
Good luck!