The Rice University Neologisms Database

Cup of tea (or coffee) UK accents make the contraction possible; it’s not as effective with an American accent. As the phrase ‘cup of’ is used multiple times a day in most British households, it was convenient to abbreviate ‘cup of tea’ to ‘cuppa.’ More recent uses include ‘cup of coffee’ in the meaning, perhaps as the word has been introduced in the States where coffee is the standard drink.