In response to the question asked, the address I used was
Mr Keith Williams
CEO British Airways
Waterside
PO Box 365
Harmondsworth
UB7 0GB
I lifted that address from the BA website so don't know whether it is the ideal address or not, but it seemed to work. I hope that the original flight booked off the island was BA linked or the "No show" fine print could be invoked for the return flight
Incidentally a week has now gone by since the Much Beloved sent details of her expenses etc to BA as they requested. There has been no further reaction.