BA have something called 'chefs chat' which includes allergy information. A couple of the BA staffers have specifically mentioned it.
And a reminder that peanuts are not nuts!
BA (well any airline) has no control over people eating anything.
As I've said before you could have someone who ate a pack of KPs finest before boarding and then starts to handle things - their seat, the seat in front, the OH locker, the toilet door, the IFE etc etc spreading the oils and particles onto whatever they touch. Those residues could be there for days and days as well.