I have applied for Greek residency, on the back of my wife being Greek, and us living in Greece (but not before the deadline for automatic residency).
It is a bit of a drawn out process, despite being almost a certainty..... There is up to a 2 year waiting list to have my application processed, (during which time I can live in Greece but not work). I am then given 5 year temporary residency, with no working rights, and no GR passport. After that 5 year period, I am then eligible for 10 year residency and a passport, though apparently the passport can take up to 7 years during that period to issued.... fortunately I only want to live here, but is a process...
Apparently there are only 3 ways for brits to move here, 1. Birth, 2. Marriage, 3. A lot of money that you will invest in Greece.