Although capable aircraft technically exist today, flying the so-called "Kangaroo Route" between London and Sydney nonstop has proven elusive for airlines, from both a profitability and a customer comfort standpoint.
First and foremost, traveling the 10,573 nautical miles between London and Sydney requires nearly 20 hours in the air at current aircraft cruising speeds, an inhumane amount of time to spend in a pressurized metal tube, even if you're lucky enough to have a lie-flat first class seat. Secondly, the fuel economics of long routes are notoriously poor, which is why most don't last long – a notable early 2000s casualty was Singapore Airlines' nonstop Singapore-Newark route (although the airline restarted it in October 2018).
In spite of this, several aviation minds and entrepreneurs believe not only that London-Sydney nonstop could become a profitable route – they believe it can be flown in four hours, or even less!
A Successor to Concorde?
If you have any arithmetic aptitude whatsoever, the obvious solution to the problem of the London-Sydney flight time is to increase speed substantially. Like, say, the creators of the short-lived Concorde supersonic jet did, when they engineered an aircraft capable of flying at 1,200 miles per hour, more than twice as fast any contemporary commercial aircraft.
As of this writing, companies such as Gulfstream, Lockheed Martin and even NASA are in competition to try and build a presumed "Son of Concorde," only this son would be a fair bit more powerful than his daddy, to the tune of 2,500 miles per hour – or maybe even faster.
The Supersonic Problem
The problem with Concorde, of course, was not so much the price flyers were required to pay or the lone (but extremely high profile) Concorde crash that occurred in 2000 at Paris' Charles de Gaulle airport. Rather, the chief barrier to mainstream supersonic flight is...well, the sound barrier, and the "sonic boom" a plane creates when it breaches it.
For flights that travel mostly over water (such as New York to London and Paris, which were the Concorde's bread and butter), this wasn't such an issue. But since London to Sydney (and, to be sure, many of the ultra-longhaul flights in the world) require travel over land masses, the parties listed above are scrambling to find a way to minimize or even erase the effect of sonic booms on terrestrial civilization.
Richard Branson's Solution
Not surprisingly, mega-entrepreneur and all-around visionary Richard Branson has proposed a solution. And in equally unsurprising fashion, his solution seems absolutely bonkers upon first read.
Branson envisions flying London-Sydney (and other super-long routes) not using a supersonic aircraft, but rather using a Virgin Galactic "spaceplane" that travels up into space, rather than through the atmosphere. Doing so would not only enable the plane to leverage rocket-like speeds as it whisks through zero gravity (Branson envisions London-Sydney taking three hours or even less), but would also have almost no impact on the environment as compared to modern-day flying.
For now, however, travelers between London and Sydney will need to "hop" like a kangaroo, with stops along the way in Hong Kong, Singapore, Dubai, Abu Dhabi, to name a few of the routings. As of March 2018, travelers originating in the Western Australia city of Perth can fly to London nonstop, though Sydney won't enjoy nonstop service to London—via space or Boeing's next-generation 777X plane—until at least 2021.