Maybe this Q might have been better posted as a separate thread.......but anyway, firstly I think you really meant to say you checked the classic awards which are 320K points for 2 pax return BNE to LHR (not ASA's). The QF system won't price out the taxes for the whole trip unless you have enough points in your account but if you do have 160K you could try searching for 1 pax to get the taxes. Alternately, you could search the individual flights to get the taxes for each leg - then just add them up
e.g. Taking just the BNE-HKG and HKG - BNE legs the taxes are $205 and $167 respectively. Total $372. You can do the same for the BA flights to/from LHR - can use QF or ba.com for this. Just do a dummy booking at ba.com for a paid Y flight HKG - LHR one way (taxes should be the same as an award flight) and the taxes show as $HKD977 i.e. $AUD134