The latest update of the GOV UK site (January 11th 2017 ) advises that anyone renewing from Greece needs to provide
Name and address and/or residency evidence. Please provide one of the following:
• visa or resident permit (or colour photocopy)
• tax record eg a letter from a tax authority
• educational record eg school report
• employment record eg official letter from your employer
• letter sent to you from a central, regional or local government department
• medical/health card
• voter’s card
• immigration documents.
Source : Applying for a passport from outside the UK (supporting documents)
Extract from HM Government news article 12 April 2013:-
We are making important changes to the way we deliver British passports. The UK government's goal is to ensure that all British nationals living overseas receive a consistent, trusted, secure and efficient service whilst keeping the costs as low as possible. In order to do that responsibility for issuing passports overseas passed from the Foreign Office and its posts overseas to the Identity and Passport Service (IPS) - an Agency of the Home Office, which already handles all passport applications from people living in the UK. From 15 April 2013, British nationals in Greece will submit passport applications to IPS in the UK for processing. All the information needed to complete the passport application process will be available on the website at https://www.gov.uk/overseas-passports .
Please note that our Embassy in Athens is not able to take calls about individual passport applications and Consular staff cannot countersign passport applications. If you cannot find the information you need on the https://www.gov.uk , please contact the IPS Passport Advice Line on +44 300 222 0000.