How to survive a Long Haul Flight
Getting to say Australasia, particularly New Zealand is going to take a rather long time. This is going to involve siting down for a long period of time. Whether you get a direct flight or not, probably going to have a lot of waiting at the airport, in the transit lounge.
Breaking the Journey Up.
This ia good option, not only would you save some money on a non-direct flight but you get to see a little more of the world on the way. Going off to see the lights of Dubai would be an awesome experience, or whether you would like to see. You could even book a night or two at a hostel or hotel and further you experience. It also adds to the experience of going around the world.
If you're flying a rather long way from London to Sydney, there are numerous options, this includes going via the middle east and going via North America. This middle east is something to be recommended.
Both mentally and physically. Be alert, and get about the cabin and take a walk or if you can't leave your seat so often exercise you legs once in while especially your feet. A small proportion of the population will experience circulation problems or even deep vein thrombosis. But don't let that scare you, really you're more likely to suffer from fatigue. Your carrier should provide you with in flight socks that aid on circulation in the legs.
Apart from that get a good book, listen to some music, watch some inspiring movie from the in flight entertainment. Or start thinking of planning your trip because you've got all the time in the world.
Don't Fly at All
Certainly if you're totally petrified of flying. You could follow the footsteps of Charlie Boorman and travel "by any means". Travel by a network of trains, ships and other means. Although that is going to require several months of planning and would be costly it would be one great experience. Until recently one company the Oz Bus company was offering a bus service from London, England to Sydney! This takes around 6 months and you would need a stack of visas. Expect to pay a fare exceeding £6,000 GBP.