A word of warning about Sainsbury's own brand products labeling:
Products may contain MORE allergy inducing ingredients than those described in the label
DS had a strong reaction to Sainsbury's' own Baked Beans and Sausages a couple weeks ago after accidentally having some at nursery. I checked the label and there was nothing there that can justify such reaction in DS apart from something that was described as "flavourings". I rang their customer service and, though very helpful, told me they could not give me the details of those flavourings because they had to protect their formulas from their competition. So after some negociating I give them the list of foods that DS is allergic to to see if they could find the item in their secret flavourings.
They come back to me saying about the tomato sauce of the beans containing MILK. DS is very allergic to milk but has never had a reaction of that kind or strenght after having it, so I assume there's another "secret ingredient" there that we are not aware DS is allergic to. However, I thought it was very important for you, who have or have children with severe allergies to milk to know about it.
Hope that helps, I don't know how to pass this information to more mothers of allergic children than those in Mumsnet, but if you know how to, please pass the word.