If you are tax resident in Greece then you are supposed to declare your worldwide income to the Greek tax authority. Exactly where you pay tax will depend on the nature of the income and how it is dealt with under the UK-Greek Double Taxation Agreement
, note this is a pdf download.
If tax is assessed in Greece but it has already been deducted in the UK then you will need to get a DTA Form signed by the Greek tax authority and submit that to HMRC to reclaim the tax paid in the UK. Greece "issues"* these forms on an income stream by income stream basis, i.e. not just a general form saying you are tax resident here. Getting them is not easy but once you have submitted one HMRC do not demand them each year, i.e. they will mark that income as NT on their records. They may ask for a verification at some point but I have not had to provide one so far and my UK pensions have been marked as NT for 8 years now I think.
* "Issues" is not really the correct word. In my case I got hold of a copy of the form, modified it slightly, completed one for each income stream and then submitted the form, via my accountant, to the Greek tax authority. Many many months later after much prodding I eventually got them back signed and, of course, stamped. I also had to submit estimated forms for the following year even though I didn't need to ask for a new form.