On my arrival I saw how beautiful and clean Australia was, how maintained the river walkways, beaches, free sports and swimming facilities are from the Aussie tax $. I made the personal choice to pay tax on all my income to Australia. In doing so (For me) there was a tax saving and less fees, reducing how complicated it would be for my tax agent to do my assessment.
See here for more detailed info on differences in having ATO not HMRC collect your taxes.
Should you also decide after research with the links provided to just pay tax in Australia, completing Form DT Individual (P85) is the way to achieve this.
ATO have data sharing agreements with UK banks. Feel free to do a web search for yourself. If you are considering trying to hide or not declare your UK income to dodge tax you risk serious repercussions if discovered.