Can I re enter into the United Kingdom on my Australian Passport (with a photocopy of my british passport) ?? I am travelling to the USA and need to leave my UK passport here to get a visa sorted out to Russia, can I get back in with out my UK Passport with out any problems?
Unlike the USA, the UK does NOT stipulate a condition that British nationals must enter with a British passport. I.e., you can use any valid passport. The motivations behind this rule are mostly rooted in various peculiarities of the Commonwealth.
You will have a landing interview with an Immigration Officer under Paragraph 41, and if successful, you'll be admitted under Paragraph 41 (unless you specifically request to be admitted under Paragraph 18 - which is emphatically not recommended).
Because your nationality is pertinent and material, you should disclose it under Paragraph 321A(2), even if the IO does not specifically ask.
Others have noted that you can expect to spend more time in your landing interview. You can mitigate this somewhat by demonstrating that you have a clear understanding of the rules governing your visit. Many people do not, and they in for a proper 'grilling'.
The current rules which contain the paragraphs I cited are at https://www.gov.uk/government/collections/immigration-rules