In my experience they will loose/ignore your letter.
Send it again directly to Rod Eddington - he has a team dealing with letters sent straight to him.
You'll starve waiting for a reply from customer services
Keep fighting
The first offer you will get will be a space available upgrade on your next BA flight. They will tell you how they have learned from your experience and will improve their training etc.
Politely decline it. - they obviously hadn't checked the aircraft over before fight etc
They will ask you what you want. (a full refund or free flight is generally a reasonable thing to ask for)
BA are just the same as any other airline- no better or worse than any of the others no matter what you read on this board.