I came to the UK at the beginning of 2009 from Austria and 2018 got British citizenship. I’ve worked all the time I’ve been here. I was born over in Austria, my parents and rest of my family are still there and I’ve got a small apartment there. Am I domiciled in the UK? Can I declare I’m non-dom on my UK return? If so, do I need to complete my UK tax return to declare the money I receive from renting out my Austria property?
It sounds as though you have a domicile of origin in Austria. If your intention is NOT to remain in the UK permanently (and there is evidence of this, e.g. strong family ties to Austria), then you probably have not established a domicile of choice in the UK. Though be aware that, since you came to the UK in 2008/09, you will become deemed domiciled in the UK for tax purposes in 2023/24.
For completing your 19/20 tax return: if your rental income is less than £2,000 in the tax year (and you have not bought it to the UK), then the remittance basis will apply automatically, and so there’s no need to make a claim for the remittance basis. This is because individuals with unremitted (i.e. not bought to the UK) overseas income of less than £2,000 do not need to make a claim for the remittance basis. This doesn’t trigger the automatic loss of the personal allowance, which would otherwise happen if a claim was made for the remittance basis.
On the other hand, if there is more than £2,000 of unremitted foreign income, and you would like to not report that income on your UK return, then it will be necessary to make a claim for the remittance basis on the tax return (this is box 28 of the 19/20 residency pages of the tax return), but this will result in losing the tax-free personal allowance (of £12,500). If you’ve paid any tax in Austria on the rental income, you should be able to claim that as a credit against any UK tax due, though you would need to check UK-Austria tax treaty to make sure that’s the case.