You can lose weight on an exclusive diet of Wine Gums as long as you are in a calories deficit but it is not healthy. "Eating healthy" is a rather nebulous phrase, but by almost any definition, will include reference to macronutrient composition of a diet.
You need a range of carbohydrates, protein and fats in your diet. This is particularly important for yourself as you are talking about a cut and make reference to resistance training implies you are focusing on reducing body fat rather than simply weight loss. If you are in a calories deficit and you are not eating a reasonable amount of protein, your body with starting catabolising your muscle tissue.
Cooking the bulk of you food is the easiest way to eat a healthy diet on a budget. Oats, rice, pasta are dirt cheap, vegetables are relatively cheap, meat isn't too expensive.