Should I take that some Cypriot Greek speakers do call Pounds sterling as “λίρες εγγλέζικες” (English pounds) because the notes…?

Cypriots refer to English pounds, for the simple reason that colloquial Greek refers to English rather than British exclusively. Note that your phrase uses the colloquial εγγλέζικη, rather than the formal αγγλική for “English”.

The formation of the United Kingdom never made much of a popular impression on Greeks. In fact even in more formal Greek, the British rule of Cyprus is referred to as the Anglocracy, Αγγλοκρατία, not the Brettanocracy.