January 6th is 'Old Christmas Day' - i.e. Christmas Day in the old (Julian?) calendar before the Gregorian reforms which didn't come into effect in England until the middle of the 18th century. Preserved in certain versions of The Cherry Tree Carol, the date also corresponds, as you say, to Twelfth Night & The Feast of the Epiphany, when traditionally we sing We Three Kings of Orient Are, or at least dig out our record of Mario Lanza's superlative rendering, which can be found in most charity shops on his Christmas Carols album - highly recommended!