Buy round the World Airline TicketPurchase the World Airline ticket.
With £4846 that's probably about 1500 less than you'd be paying for a similar 4-continent Oneworld Explorer RTW (which you can buy on-line using the Oneworld on-line tool) with the UK as the start/end point. This is because this fares only up to 29,000 mile, and limits you to a few stops.
It is certainly a good deal (compared to a "normal" London to Oz back home B.C. trip), but it is relatively limited in kilometres and itinerary. Compared to that, if you began in another land, say Egypt or Israel, you could buy a 4-continent ticket for about the same cost, which would give you twice as many stations, and the possibility to jump around in North America, Asia or Australia/NZ, much more than the BA/Qantas ad for.
Why should one now make the efforts to cover a long stretch in order to simply take off again with a foreign ticket? 2 month later you end the journey by going back to Jordan (or Israel, Dubai, Egypt or anywhere else in the Middle East). Done. Now, this may seem crazy, but if you want to see the world, it's a hell of a store, with 16 bus ticket classes (First on U.S. home flights) for about five Gs, or something like 313 pounds per one.
Thirty hundred pounds for a business-class plane between Melbourne and LA? I am a member (i.e. junkie) of the American Airlines FF programme and I normally purchase one of these 4 Continent BPLs every year or 18 month. And because all my flights in premier staterooms earn me enough points to achieve and sustain AA rating excellence, every single point I earn is matched (actually 225% or 250% by adding the " Classic of Serve " award miles) in points I can use.
An itinerary like the one I've described will make something in the 125,000 AA mil region that I can turn over and use for a great roundtrip between the U.S. and Europe or South America, or another 5000 mile ( readily available through Visa Bonus, etc.) can be added and 130,000 mile can be used for a New York - Paris - Hong Kong - San Francisco - New York way of doing it.
It may work for you, it may not work for you, but if you are willing to think about a multi-year horizon, and like the liberty and convenience of travelling on your own, it may be worth considering.