OP does sound Australian with a conscious effort of not straying into the rising intonation pattern (which would be annoying).
I am a Londoner myself so am exposed to multiple accents on a daily basis. I can definitely tell the difference between the Ozzy accent, the Kiwi accent and the South African accent. To the unfamiliar ear, all three could be mistaken for the Ozzy accent.
Methinks that the OP has been watching too much Neighbours and Home And Away (Australian soap operas) during her stay here.
The key to getting a British English accent (or any accent) is to hear the "music" of how the language is spoken.
I would advise foreigners wanting to attain the British English accent, that they'd go for the slight RP version of it - BBC News with a hint of Queen's English.
Audrey Hepburn, Omar Shariff and Michelle Yeoh all have elegant accents with just the right amount of gravitas in them.
For an alluring, speaking and singing accent, go for the Scottish accent as voiced by Shirley Manson and Hannah Gordon.