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Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
Can you just confirm that you intend to live in Greece.
Assuming you meet the criteria to be treated as non-UK resident for tax purposes, you will only pay UK tax on UK source income such as your rental income. As you are UK domiciled, you will be entitled to the UK personal allowance. Remittances of non-UK source income to the UK will not be taxable in the UK so long as you are not tax resident in the UK.
I hope this helps but let me know if you have any further questions.