So the summary, at the moment, for people who have a cancelled flight within 72 hours (I waited on the advice of the FAQ here), and if you want a refund, and are not status (just dropped from Silver), that you need to work out what time of day you'll get through the standard BA line (0800), press 2 2 2, and actually get into the queue.
After 7am? Lunchtime? Early afternoon before US lines open (East coast, 7am is noon UK)? My flight was Friday evening.
I'd like to get his off my chest before tackling the Qatar flight (if they can rebook it sometime nice like over Christmas and drop me back at BHX, I'll rebook).