Your question broadly come in three parts: tax on rental and other types of UK income, tax on disposal of property, and taxation relief between Australia and the UK.
The answer aims to provide information on where you can find more information to fulfil your tax obligations. Though it looks to me that it is in your best interest to find a tax advisor to ensure your tax affairs are fully compliant, given the situation you are heading into is not the most trivial.
Tax on rental/investment income
As of Tax Year 2018/19, income arising from UK, especially rental income for a property in the UK, for non-resident is taxable in the UK:
You need to pay tax on your rental income if you rent out a property in the UK.
The only income that is explicitly exempt from tax when one lives abroad are the state pension and income from gilts:
When tax isn’t due or is already deducted
Non-residents don’t usually pay UK tax on:
- the State Pension
- interest from UK government securities (‘gilts’)
For dividend income, while the Government has not explicitly mentioned they are taxable, as dividend income is normally taxed in the UK as part of your income, I'd assume dividend income should not be an exception.
The confusion probably arise as dividend income used to arrive in one's account with tax already taken off - this is no longer the case, as started right after the "When tax isn’t due or is already deducted" paragraph quoted above:
Income Tax is no longer automatically taken from interest on savings and investments.
If you are citizen of any country in the EEA, you will get the tax free personal allowance:
You’ll get a Personal Allowance of tax-free UK income each year if either:
- you’re a citizen of a European Economic Area (EEA) country - including British passport-holders [...]
Tax on disposal of residential property
You also need to pay capital gains tax in the UK when you sell your property in the UK. The exact procedure (and possibly the amount of the tax you end up paying) differ slightly depending on when you sell it.
If you sell it before you emigrate, the usual reporting procedure via self assessment applies. If you are no longer a resident in the UK for tax purposes, this guidance applies instead. They are long guidance and hence I will refrain from citing text from these two documents.
Taxation between Australia and the UK
If you are a non-resident in the UK and rent out a property, chances are you will be doing so via a letting agent and income arising from letting out are taxed at source (think of it as a pay-as-you-earn) under the Non-resident landlord scheme.
The double-taxation agreement between Australia and the UK provides means certain relief is available for UK property income received by non-residents of the UK who are residents of the territories listed in the table. You just have to claim it back.
This guide provides a (perhaps not the most user-friendly) overview to what sort of relief is available. In the OP's case, one only need to note in Page 2:
Where a percentage rate is shown it is the ‘treaty rate’. The relief from UK tax is the excess of the UK income tax over the treaty rate. The basic rate of
UK income tax is 20%. So if (for example) the treaty rate is 15% then the excess of 5% tax is relievable if a satisfactory claim is made.
and the percentage rate shown in the cell in row 'Australia', column 'Property, Income, Dividends' (page 7):
This means if you are a basic rate taxpayer in the UK, you get a 5% relief. This number is 25% and 30% for higher rate and additional rate taxpayers.
If you have other investment income, especially something related to Property Authorised Investment Funds, some exception applies on tax relief related that particular stream of income. I guess you will need a tax advisor in that case.