In terms of price, you're probably going to be best off booking a LHR-SYD return ticket on BA with stopovers in SIN (outbound) and HKG (return). Most fares should allow this.

Then book a SYD-NAN-BNE (or vice-versa) ticket on Fiji Airways (you could buy it as the Qantas codeshare, but directly from FJ will probably be cheaper). Finally book a one-way SYD-BNE (or vice-versa).

Without knowing dates or other details, that's generically the first thing to check price-wise.