I am studying in London for under 6 months. I am an Australian citizen so I do not need a visa to enter while I study. I am allowed in the country 10 days before my course starts. My partner and I need to find a place to live while I am studying.
Am I allowed to enter the UK for 2/3 weeks to look for a flat, leave for a week and enter the UK as a student providing all my documents for my study?
As that will be the start of the 6 months. We aren't able to find a clear answer anywhere.
Take note that the Student Visitor and Extended Student Visitor routes are being abolished on 24 April 2015 (about 6 weeks from now). They will be rebranded and moved from Part 2 to Part 3 of the Immigration Rules slightly before then.
New guidance will be (or is expected to be) published later this month. You will need to check for their publication to be sure that you still qualify. That may explain why you are having trouble finding relevant material on the net.
For your question about arriving as a visitor for two weeks, and then arriving again as a student, this is fine as long as you clear both landing interviews under the rules governing each entry. You didn't give dates in your question so whether you qualify will depend upon which rules are in effect on each of your entries. In general, they prefer if you perform the accommodation search and study all in a single visit, but there's nothing in the rules specifically prohibiting what you are planning to do.
Also note that depending upon where you plan to live, the new 'right to rent' rules may be activated. For some people this means 2/3 weeks may not be enough time to find an agreeable landlord. The roll out of these rules is geographic and has already started in Birmingham for example.
All halls of residence (whether the landlord is an educational institution or private accommodation provider) are exempt from the Scheme, as is any accommodation provided for students directly by a higher or further educational institution. Residential tenancy agreements are also excluded where a student has been nominated to occupy the accommodation by a higher or further educational institution, or a body established for charitable purposes only. Such a nomination could take a variety of forms but will require communication between the institute and the landlord providing confirmation that the student will take up occupation under the residential tenancy agreement. Landlords should retain a copy of the nomination document relied upon to support a claim to this exemption.
