Just before Christmas we moved to another village on Rhodes. Three days ago a new police station opened in Kalithies. Two police officers there , have told us that as we hold EU passports from the UK we do not need to apply for Greek Residency Certificate.
As far as I understand it, technically anyone living in Greece (or any other EU country) for over six months and anyone living here for a shorter period who wants to work should have a residence permit.
They are quite straight forward to get as all EU citizens are entitled to residence in any European country.
Lots of people don't bother but you could get into trouble if you work without one and there are times when they are useful - to buy a car, for instance.
You should also register that you live in Greece with the British Embassy. You can do this online via their website I think.
According to The British Consul the permits are now cream & do not have to be renewed. You need one to buy certain things like cars or motor cycles , but apparantly not a house. The police are in some places not up to date with things or cannot be bothered to do the paperwork.If you do need help in obtaining one The British Council will get in touch with your local police chief.