> as conkers are seeds (not a nut) - so shouldn't be an issue for someone with a nut allergy
I take issue with this, and in fact we can see how the pedantic scientific meaning caused confusion about the actual underlying facts: people with allergies to what are commonly called "nuts" can in fact be allergic to things that according to the pedantic scientific definition are "seeds". So the OP is actually wrong to say it shouldn't be an issue for someone with a nut allergy!