Our childcare centre has a policy that we are not aloud to bring food to the centre. All the food is dealt with in their own kitchens.
They have a list of names in the kitchens with all the allergies the children have and what they are aloud to have.

Some parents may even choose that their child can only have brown bread not white and no yoghurt for instance.

I think you could to talk to the director who will then intern talk to all the staff and make sure there is always an eye on your child during meal times and that every child washes their hands after meals.

It is so tough though as even with the strictest centres there is always a chance something could get past. They just need to make sure they know how to act swiftly and calmly in an event.