Welcome to FT
loui
I'm a little confused. Both QF and BA fly every day (several flights in fact) to the UK. Is it that you already have a booking on a BA flight, or no seats left (at the price you are willing to pay) on QF flights?
As for upgrading, generally you can only upgrade using the airlines own miles/vouchers/upgrade credits, not anything from their partner's frequent flyer programs. Hence for members of Qantas Frequent Flyer selecting QF flights in order to be able to upgrade.