It sounds like the CAA is overreacting, perhaps because nut allergies are so much in fashion these days.
There are a couple of things to keep in mind. First, you don't know if you have an allergy until your first allergic reaction, so there may well be pilots with severe allergies flying who don't know about them. Second, food allergies generally only produce a reaction when the allergic person actually consumes the food. The mere proximity of that food or the smell of that food isn't enough, despite many apocryphal stories that assert otherwise. Third, anaphylaxis is rare in food allergies (actually it's rare for all allergies); you're more likely to stroke out during a flight than you are to experience anaphylaxis, even if you actually munch on a food to which you are allergic (unless you actually have a prior history of anaphylaxis). Fourth, psychology is important in allergies: allergic reactions can be psychogenic as well as physiological … a person with asthma can experience an attack simply from emotional stress, for example, even in the absence of any allergen. And a reaction trigger by an allergen can be worsened by psychological stress. This makes it hard to prove that an attack actually results from exposure to an allergen, in some cases.
The priorities of aviation medical authorities mystify me at times. It's as if they base their disqualifications on what they can detect, as opposed to basing them on what might actually incapacitate a pilot. Smoking is a lot more likely to kill a pilot during a flight than a food allergy, and yet being a smoker doesn't disqualify someone from being a pilot.