It is named after a small cup for serving after‑dinner coffee.
1 coffee cup is 21/2 British imperial fluid ounces.
[1] Five British culinary measurement units are related to the coffee cup: the tumbler (10 British imperial fluid ounces),[2][3] the breakfast cup (8 British imperial fluid ounces),[1][4] the cup (6 British imperial fluid ounces),[2] the teacup (5 British imperial fluid ounces),[1] and the wine glass (2 British imperial fluid ounces).
British cookery books and recipes, especially those from the days before the UK's partial metrication, commonly use two or more of the units above simultaneously: for example, the same recipe may call for a 'tumblerful' of one ingredient and a 'wineglassful' of another one; or a 'breakfastcupful' or 'cupful' of one ingredient, a 'teacupful' of a second one, and a 'coffeecupful' of a third one.
There is no British imperial unit–based culinary measuring cup.