You can only use the Visa Waiver scheme if you have a machine readable passport. On UK passports this is indicated by two strips of letters, numbers and symbols at the bottom of the photograph page. All passports issued in the UK within the last 5yrs at least (probably a bit more) are machine readable but not sure if Greek ones will be. If it ain't machine readable you do need to get a visa.
Dunno if anyone has already posted this, didn't read all of the thread.