I don't know what day you were calling (I am assuming from the US), but I had similar problems on Monday. Exec club line was just engaged after selecting options.

I had an email from BA asking me to call them...didn't get any sense from the Indian call centre - they were telling me my flight was cancelled (which was confirmed as complete rubbish).
Later that day I decided to book a multi city trip with 1 leg UuA, after some failed attempts I did finally get through to the Exec Club Blue line (in Newcastle) who were extremely helpful, grabbed the last two remaining award seats and booked it all no problems (also waiving the booking fee as it couldn't be done online).