Definitely try Aldi. Loads cheaper than the main supermarkets. Quality is fine, if you're finding meat going off within the use by date, check your fridge temperature, I've never experienced that.
If you're 'suspicious about chemicals' then avoiding processed food is probably what you should be aiming for as a priority. The 'time' problem can be largely solved by batch cooking, also get as much veg into each meal as possible, also helps with the cost. Eg instead of making chicken curry, make a chicken, chick pea, spinach and potato curry. Look up tray bakes or slow cooker recipes that, while might not be any quicker overall, you don't have to stand and stir them like you do hob recipes.
Morrisons has got expensive now. Although someone on another thread mentioned that they do fresh ready meals that are basic ingredients, eg fish and vegetables that don't have a lot of processed ingredients, but it depends how many you are cooking for. Would be good for 1 or 2, but no good for a family.
Frozen veg definitely helps reduced prep and cost, and waste. But not all of it that nice. We like spinach, edamame beans and green beans best. Also the steam fresh frozen packs of veg/rice.