Preservative-free Foods. Preservatives must be listed on labels, so check the ingredients list before you purchase processed foods. Most organic foods cannot contain preservatives, and whole foods, including fresh and frozen fruits and vegetables, eggs, milk and non-processed meats are free from preservatives.rganic fruits and vegetables don't contain preservatives. A study published in Lancet in November 2007 found that a preservative called sodium benzoate may increase hyperactivity in children.