It does exist! An unspoiled island with a very Greek flavour, relatively few tourists, excellent sandy beaches, a characterful port, and a direct flight.
Lemnos lies halfway between the shores of Asia Minor and the slopes of Mount Athos. Indeed you can see Athos on a clear day, and they say that the holy mountain casts its shadow on Lemnos twice a year.
Getting to Lemnos Saturday Day flight Gatwick to Lemnos. Then 40 mins by coach or taxi. It is also possible to fly from Heathrow via Athens (daily flights) – supplement on request.