With the amount of people wanting award seats on Concorde I'd expect some trouble getting an award seat, certainly during high-season and around the end of the year. There are not that many award seats available per flight...

I'd suggest calling Qantas to see what they can do for you, although I wouldn't expect them to be able to get BA to release extra seats for them, if BA ever releases extra award seats it's for their own top tier members.