I'd certainly write in and send the receipts (keeping copies for yourself).
Its certainly something Customer Relations will have dealt with many times before.
Unfortunately in some airports, particularly those which are either very old, very congested or in countries with monsoon like conditions it does sometimes happen that the baggage carts get left for too long outside.
For this reason I used to always ensure my suits were inside those plastic bags from the dry cleaners, or ideally use a hard case.
BA will record the complaints statistics for things like this and can then take action with a ground handler if the problem seems prevalent in one particular airport.