Can I just clarify what type of upgrade you are seeking? Just to check you are seeking to compare like with like!
As I understand it, on some US carriers they automatically upgrade elite level fliers to F if there are seats available. That is not the way BA does it, to keep the exclusivity of the F product.
Are you calling and just asking to be upgraded (US style), or are you calling asking to be upgraded using cash or using miles (UUA)? As others have already given you the info on redemption/upgrade inventory I wont bother repeating it.