You need to be very careful about which countries you are taxable residents in, it is possible to be a taxable resident in two different countries that overlap or a taxable resident in neither.
For Australia to be a taxable resident you need to be physically present in the country for 183 days of the tax year the UK has similar requirements but it's tax year ends on the 5th April as opposed to Australia at 30th June. If you've just arrived in Australia you should be a taxable resident for 20/21 so long as you don't spend another 76 days between now & 30/06/21 in another country. e.g frequent business trips to NZ. https://www.ato.gov.au/Individuals/international-tax-for-individuals/work-out-your-tax-residency/
A word of warning don't believe everything a tax agent tells you, they may be wrong & if they are all the penalties are payable by you not them. So you're best to confirm independently what they say. Also they can only advise based upon what you tell them, you may inadvertently omit a crucial piece of information that may change their advice. Even advice from the ATO does not void any liability if it is wrong & you act on it!
If you have a complicated tax situation I wouldn't just go to a fixed price tax agent, I'd seek a professional tax adviser at an accountancy firm etc. The extra money you pay may only be a few hundred dollars more but could save you thousands , particularly if you have a property sale in the tax year.
One last piece of advice, don't rely on anything posted on an internet BB!
