So the obvious answer is that the British and Turkish presence on some of the Aegean Islands, Crete & Cyprus is because it was relatively recent. That being said the Greek presence is the oldest and is present, so why wouldnt the Venetians or Genoese presence be apparent?
An easy example is Cyprus, people from there identify with the British because of their long presence there and that many of the local population know English (British Cypriots). The same applies for the Turks as many Greeks converted to Islam though out the Ottoman empire to not be discriminated against and also immigrated to a lot of the current Greek islands. So why is there no Italian characteristics in the local population such as in Crete, Naxos, Paros etc.?
Or in other words what were the Italians doing on the islands that made it so that no Greeks on the islands past, present or future would ever identify with them?
For Cyprus it may be because they resent the Venetian rule of their island. Their queen, Caterina, abdicated her throne and gave the island to Venice. Venice, in turn, heavily taxed the island and restricted movement in the political hierarchy to only allow Italians to have the upper positions and kept the Cypriots in the lower positions. In 1562 a rebellion rose up against the Venetians and was put down fairly rapidly. The only good they did for the island was try to prepare it against a Turkish invasion and those preparations were lackluster until about 1570 on the eve of invasion when more actions were taken. Even then the island still fell to the Turks who were no better than the Venetians when it came to ruling the island. The only reason why there are so many Turkish descendents and converts is because the Ottomans tried to move people there from Anatolia early on as opposed to the Venetians who didn't send a lot of settlers.
For reference,
1982 Footprints in Cyprus by Sir David Hunt