Hi DistantRumble,
Check out this link;
http://flyaow.com/classavailability.htm
and enter your flight detalis.
If numbers to the right of Y read 0 then the flight is likely to be full.
However on British Airways it will help if you have status(have you got a Eecutive club card?)
If you are in WT then you are likely to be upgraded to WT+ only ( double upgrades are rare but they can occasionally happen).
If you are in WT+ then you may have a better chance of being upgraded to Club World.
Regards
TBS