Point of order - unlike a hospital or a local authority, a private company such as Heathrow, while it can still charge you for parking or pretty well anything else it wishes to, can only issue "fines" if there is provision in their byelaws to do so. So far, there is no sign of Heathrow amending
theirs, so we don't know exactly what the provisions will be.
Failing provision in the byelaws, while there will clearly be repercussions from any non-payment of the drop-off charge, then rather than a penalty or a fine this will take the form of a "charge notice" i.e. an invoice (presumably with an incentive for early payment) but which can only be enforced by going to court. Heathrow's contractor will also need to show that the amount of the charge is proportionate to the loss incurred.