Having worked in BA Customer Relations where I had to deal with strongly worded letters every day, I don't think you should necessarily worry about 'annoying' them as such.
Basically, BA are at fault and should refund the amount that they overcharged. However with regard to fees and interest, the airline will claim that this is out of their control - which in effect it is as it is a consequential loss - so therefore they will not compensate for that. What they will do, if you ask them, is provide a statement of what happened so that your bank will refund charges.
As for wording, just stick to the facts with a request for assistance but leave emotion or threats out of it. It probably wouldn't hurt to address it to Willie Walsh. If you have an exec card, include the number. Include your phone number as well, as they are prefer to call people rather than write as it is helps resolve cases quicker. Hope I've been of some help.