I think the main choice is whether you go non stop with someone like BA, JAL or ANA (all probably at a premium price) over a direct flight via the Middle East or mainland Europe. Generally, of those 3, ANA is best regarded. Lufthansa / Swiss have been offering some very good prices recently to Australia . With the direct flights (as opposed to non stop flights) that does open up the option of other local UK airports if that works better for you.
I found, for Business class to Australia, Celebrity were about £500 per person more expensive compared with the same flights bought via a UK travel agent and the flights didn't open up as quickly as they did through a UK agent. I suppose the advantage is that with Celebrity it is a package deal so if the flight or cruise is cancelled you can cancel the whole thing. With our slightly cheaper tickets it is not a package. If the cruise is cancelled we still have to fly. If the flights are cancelled Celebrity will still expect us to get to the cruise port.
I was monitoring flights and prices for ages beforehand and literally bought the flights the day they were released as I knew the price being offered was a great price, trust your own research - I've had TA's tell me in the past that £2000 for a return Premium Economy ticket from LHR to JFK was a "great price" - when I knew that it was anything but.
5 months after booking, and 7 months out, minimum prices for our flights to Australia have gone up by about £1100 per person, our specific flights have gone up by almost £2000 per person. It usually pays to book early, but my advice would be to do your research and work out what is a good price and grab it when you get good flights, with a decent airline and times that work for you (flight times can vary form 11.5 hours non stop, to over 40 hours in some extreme cases). Google Flights is pretty good for this.
For November 2022, £500 - £600 for a one stop flight is about average in Economy - £2200 in business but this might rise to about £800 - £1000 for a non stop flight, to £3000-£4000 in business