As a UK Citizen, you are eligible for Transit WithOut a Visa when transiting through Australia, provided that you meet all of the following criteria:
- will arrive in Australia by aircraft
- have a confirmed ticket to leave Australia to travel to a third country by aircraft within 8 hours of arriving
- have valid travel documents to enter that country
- must not need to clear immigration or leave the airport transit lounge for any reason before boarding your onwards flight. Even if you meet all other criteria, including being of an eligible country, if you need to clear immigration, for example to collect or transfer baggage onto, and/or to board, your onwards flight, you will need an Australian visa to do this. For more information see Transit facilities at Australian airports.
Luckyly SYD airport has TWOV facilities, although the aiport does not 24h, but this is not your case since you are arriving and leaving in the morning of the same day:
Sydney (SYD), Cairns (CNS), Gold Coast (OOL)
Do not operate on a 24 hour basis and overnight stays are not permitted. Passengers transiting overnight will need an appropriate visa for Australia to leave the airport to access overnight accommodation.
There are airport transit lounge facilities that allow TWOV eligible passengers to connect to their onwards flight.
So everything depends on whether or not you need to clear customs to board your outgoing flight to Fiji, and that depends on whether or not the journey was booked as a single ticket. If so you should have all of your boarding passes once you check-in on the first flight. If you have any doubts, ask the airline directly.
For additional information, have a read on the SYD airport dedicated webpage.