there is no point in simply calling the manufacturer the first time you try something new because it may well change before the next time you eat that food. And the manufacturer can assure you the food is free of nuts and made in a nut free factory but it only takes one food handler to eat nuts and you have contamination.
Tescos say they can not control the way ingredients are stored before they get to the factories therefore they cannot state categorically that ingredients are nut free. It would be easier for them to label everything "may contain" as some other supermarkets do.
Unless you grow and rear your own food you cannot be sure it is nut free. That's why we have epipens. After my child's recent anaphylactic reaction the consultant suggested it may have been caused by food fed to the chicken. How many manufacturers do you think go that far down the food chain (if he was right and I wouldn't trust him)?
There are other studies besides the BMJ one. They give similar results. If you want to find out more there are suggestions for the reasons some children outgrow allergy in articles like this one (which I don't claim to understand)
"Peanut-allergic donors show Th2 polarization of cytokine production by peanut-specific cells (IFN-gamma (low), TNF-alpha (low), IL-4 (high), IL-5 (high), IL-13 (high)). Conversely, nonallergic children and children who have outgrown their allergy show Th1 skewing to peanut antigens (IFN-gamma(high), TNF-alpha (high), IL-4 (low), IL-5 (low), IL-13(low)), similarly to nonallergenic food antigens (beta-lactoglobulin, OVA). This finding suggests that peanut antigens do not intrinsically induce Th2 skewing, but that the type of response depends upon the donor's allergic status."