Presumably you mean that you have an APEC Business Travel Card? Also presumably you're a resident of Hong Kong (as that's the only way that a Brit can get such a card)?

Fiji airlines check-in staff will most likely be familiar with the ABTC cards.. The catch is that normally airlines use the Timatic system for checking visa requirements, and normally it will show a specific entry for a visa exception for holders of an ABTC, however this does not show up for British Citizens, as Brits can't get ABTC (other than the HK PR version). The only "Visa Exceptions" listed in Timatic for UK Citizens is holding an ETA.

I suspect the saving grace will be the fact that Australian visas are all electronic, and the relevant visa checks are automated. When they run that check it should automatically detect that you have an approved ABTC for 'AUS' and give an OK to board.