The other option - if you can't get business class availability from London (but want to travel in that class), and if you have the time and inclination, is to fly out of a nearby foreign port (such as AMS, BRU, CDG, etc) instead, the savings in Air Passenger Duty will probably then pay for Eurostar or extra flight to get to that starting point.
And if you do this, I would be remiss in not suggesting then the best way for this is to take a one-world award ... xx_-KUL/stop/KUL-SYD/stop/SYD-YYY-LHR/ would still leave you with two more stops and perhaps 12-13,000 miles to play with (so you could then, for example, do another trip months later to US, or even somewhere like Bangkok), as long as you ended up back in the starting point.