There was a sizable minority of Greeks still living in Istanbul (Constantinople) in 1955 during the Istanbul riots. These were against the Greek minority (put together more or less by the Turkish government) and were in fact the "nail in the coffin" so to speak to being able to get by in Greek alone. There were only a few dozen deaths at most, but it served as a signal fire to the Greeks still remaining that the time to leave would be now. As far as the numbers who emigrated from the city I couldn't tell you for sure, but these riots did expediate the slow trickle into a steady pour. I hope this helps, but my degrees are in Ancient Mesopotamian history with a dash of WW2.

Edit: auto spell

Edit edit: there was about 70,000 Greeks living in the city before riots. This dropped to around 50,000 by 1960 and continued to decline to where today under 4,000 still live in Istanbul.

I wish I could tell you the exact moment when Turkish overtook Greek, but if I had to hazard an educated guess I'd say just before/after WWI was when this process began. There were a few smaller wars (Greek War of Independence) that swung the balance back and forth, but in the city itself most Greeks were treated more or less decent until around WWI.