Just a thought - why not just fly in whY BNE/SIN/BNE & make the booking on QF via the
www.expedia.com.br website. You can use the Google Chrome browser to translate into English. Read the thread below for further details:
http://www.australianfrequentflyer....rfares/qantas-syd-mel-sin-510-a-48002-16.html
You could then get a price in PE OR J ex SIN to LHR & return & just buy two separate tickets. QF in BNE would be able to through check your bags onto the BA flight even if it's two separate tickets as both carriers are members of the OW Alliance.
Ex LHR BA are known to be difficult ie refused to through check to other OW airlines when they are going against the OW policy so you could maybe have a stopover in SIN on the return leg or maybe both ways.
What dates are you looking at travelling