This is for anyone wanting to teach in Greece. You do not require a TEFL qualification, although obviously it would help you in a practical and personal way if you have no teaching experience. Legally, you need a degree (any subject) from a recognised institution; recognised, that is, by DIKATSA, which is the section of the Greek Ministry of Education responsible for validating degrees from foreign universities. They are a bit behind the times and you may find that while degrees from, say, Southampton University are recognised, degrees from what used to be Portsmouth Polytechnic are not.
What IS now required is an "Ellinomatheia" (Knowledge of the Greek Language) diploma. This new law was introduced in 2007 and foreign teachers without this diploma were deemed illegal. Schools employing such teachers could be fined and even lose their licence to operate as a foreign language school. The law has been challenged in Brussels but the ruling was that Greece has the right to govern its own internal affairs.
In the provinces, this may not be strictly enforced. In Athens, spot checks were carried out in schools in 2007/8 to see whether foreign teachers were suitably qualified according to the new legal requirement.
You may still find a teaching post but may find yourself legally employed as a gardener or window cleaner! This also used to be the case if you didn't have a degree recognised by DIKATSA. My main point is that you don't legally need a TEFL qualification.
