The actual "disease" here is affluenza, or perhaps it's anxiety that overprotective mothers project onto their children. I grew up in a small town, had pets, played in the dirt every day. Nut allergies were unheard of. It's also very interesting that farmers and dirt poor people in 3d world countries don't get these allergies. This is a problem that city dwellers construct. It's called the hygiene hypothesis.
It is very suspicious that neither the BBC article nor the Lancet abstract report a mortality statistic. Is there some problem counting bodies of people who drop dead after nut ingestion? Please don't quote me the stupid 150 deaths/year number one sees in peanut allergy articles here in America. That number was an extrapolation from a single study done of farmers in a county in Minnesota. There were no deaths from anaphylactic shock identified in the study. Somehow, the authors waved their hands and estimated 150 deaths/yr in the entire US. Meredith Broussard covered this in an article published in Harper's in Jan 2008, "Everyone's Gone Nuts." It's behind a paywall, unfortunately. I recall that the article quoted a statistician at the CDC who said there was no more than a handful of deaths in the US from anaphylactic shock in a year. Of course, the food allergist nut cases (pun intended) attacked her in droves.
There is an article by Broussard online. It covers the money trail and details how some people profit from the nut allergy scare.
I think the nut allergies are a bit like the terrorism scare. It is massively overblown. Falls in bathtubs and lightning strikes are far greater threats.