In order to have residency you have to physically reside in australia for 186 days. Then you are a resident for Australian Tax Purposes.
If it is a company then it has to be registered in Australian and one director has to be a permanent resident here.
So if you wish to live here you have to obtain a visa that allows you to live here.
You can only have resident in now country. If you live here you will pay tax on your worldwide income and you also will pay tax in the UK as a non resident on the income generated there.
Citizenship does not determine residency. Residency is where you physically live and have a home.
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