Hi,
You can apply for a letter of confirmation of residence here:
How to apply for a certificate of residence to claim tax relief abroad
These letters are issued where there is no foreign income, but there is a tax implication. You can submit a request covering from the date you arrived in the UK to the date you submit the request. Do no ask for a date in the future, as HMRC cannot predict what will be the case in the future.
If split year treatment applies, then you do not include your Greek earnings in the tax return, as they are only taxable in Greece.
Thank you.