Actually, BA has good availability as they guarantee reward seats on all flights to LHR and LGW (at least 8Y, 2W & 4J) although not all of those may be released to QF members.
The problem is that QF rarely release any seats so those available on BA are usually snapped up the moment they are released, especially for the European summer months. If you were looking 9-10 months out, you were around 2 months too late. A friend who recently flew in J to LHR watched BA availability SYD-SIN-LHR everyday for a couple of months; and everyday there were at least 2 x J available on the QF website and by the next day, the previous day's release were gone. He grabbed seats on his preferred day the moment they were released.
