If you're ever going to spend more than half a day in London, having an Oyster card (the smart card used for the Underground, buses and trains) is absolutely essential. Save yourself queuing and hassle by ordering one before you head off.
As a tourist, it's often tempting just to buy individual tickets in a foreign city, but in London, that's a costly exercise. A single Zone 1 tube trip costs £4 with a paper ticket, compared to £1.60 on an Oyster. The system also has an intelligent pay-as-you-go module: if you spend more than the value of a daily pass in a single day, the value gets capped at that amount.
There's a £2 activation fee, and delivery to Australia takes around 12 days, according to London Transport. Arm yourself with one of these and you can jump straight on the tube at Heathrow, rather than queuing with your luggage and cursing the world at large.