The tradition was imported in Greece around the 1830s, by the German-born King of Greece.
Now, about Cyprus, an other source I could find says that "it took a century after Greece adopted the tradition for Cypriots to do the same", which, assuming that both sources agree on 1830, places Cyprus to 1930. And pretty much everyone currently alive was born after that, so noone is left to find that tradition 'foreign'.
But yeah, I am sure the English influence wasn't negligible. After all, every year every house buys this shit that noone really likes[bias]. The Levantine, Greek and Turkish Cuisine are vastly superior even in Christmas
