The journey would be a minimum of two stops with LCY as the start point, of course it would be non stop if you flew from Dubai and didn't count the flights to get there as part of the journey.
A flight from LCY would save on air passenger duty as long as there was a 24 hour stop over or separate tickets were made.
A flight to any European hub would give you the choice of most of the Asian and Middle East airlines.
Any European airline showing flights to Australia is through a code share and it may work out cheaper to buy the ticket on the airline not operating the flight.
A premium ticket would give a decent amount of miles and any alliance membership would be worth taking into account.
Flying to Bangkok and then Australia on separate tickets would be worth getting a quote for as business travel to/from BKK is cheap.
Malaysia Airlines are showing some very low fares at the moment, I was looking at SIN - LHR return and they were cheapest in economy and second cheapest in business after Air India.
Flying from Heathrow or Gatwick is considerably cheaper, gives the widest choice of airlines, least number of stops and shortest journey time. China Southern from Heathrow is coming in around GBP2500 rtn with some of the flights code shared on AF or KLM.