I posted in another thread, after having similar issues, that calling 020 3250 0145 got me through at 14:50 on a weekday. What I do find surprising reading all the stories and reports on FT is it seems once in the queue the wait time isn't actually that excessive (mine was 15-minutes and reported here
toadman had 'only' 25-minutes). I'm used to waiting much longer with other companies during normal times, so why is BA forcing the queue so short? Surely most people would prefer to be in a queue rather than cut off and having to keep trying again and again with no knowing of getting though? Is it a quirk of a specific phone system they use?