Determine the type of visa you would like to apply for in order to live in London. The UK Border Agency website supplies a list of work and migrant visas that Australians are eligible to apply for. These include the 2-year "Working Holiday" visa for Australians under 30, student visas, visas to start a business in the UK and immigrant visas using the points-based system.
Establish a sponsor for your visa, whether work-related, school-related or family-related. The Border Agency requires some proof of your intentions in the country before they can issue a visa in any category.
Complete your visa application and send it to the UK's High Commission in Canberra.
Find accommodation before you arrive. This might be in the form of a hostel with weekly rates that will allow you to save until you find a more permanent place to live. If you are retiring to London, or are establishing a business, you might consider buying or leasing a flat or house.
Pack and ship your necessary belongings to your new address. If the address is a flat or central city location, have them shipped "ground," a slower method of shipping, to insure that you arrive in the UK before your boxes.
Determine your arrival date and book an airline ticket to London. You can travel to Heathrow, Gatwick, Stansted or Luton airports, which are all outside the city, but offer reasonable transportation options into London. Heathrow is the only airport connected to London by the underground metro system.
Pack your travel bags with your short-term necessities--including copies of your visa, passport picture page, letter of employment, acceptance to a university, or family member sponsorship--and take your flight.
Register for a National Insurance number by filling out the application and interviewing with your visa and picture ID at a London Jobcentre Plus.
Transfer money from your Australian bank account to a British bank. If your bank has locations in the UK, you may be able to transfer money directly without setting up a new account. If you have to register for an account at a new bank, you will need your visa documents copied and your National Insurance card handy in order to set up the account.