The whole “Twelve Days of Christmas” song comes from the twelve days between Christmas Day and January 6th (Epiphany). In the Regency, Christmas was more of a religious celebration but Twelfth Night (either January 5th or January 6th—no one seems to agree which “night” it is) was a party. They had Twelfth Night Cake or what we call “king cake” in New Orleans. There were parlor games and balls, and a good time was had by all. Maybe that’s why the last four days of the song are about lords leaping, ladies dancing, pipers piping, and drummers drumming. Partay!!
For Twelfth Night in Regency England, the custom of choosing a king and queen from whomever got the bean and pea in the twelfth-cake evolved into choosing characters out of a hat to pretend to be for the evening, a sort of masquerade. In some cases, they wore masks and the person was required to remain in character the entire night. Sounds like fun to me.
The term “Boxing Day” actually shows up during our period, but the concept of giving a “box” to the poor or to those in service began much earlier, at least as far back as the Middle Ages. I read an account from the mid-18th century that described a man with a comfortable income giving anywhere from a shilling to a half-a-crown to servants and several merchants he had dealings with. On a large estate, the owner might give boxes of food and other gifts to each tenant and servant. It mirrors the American practice of offering Christmas gifts to public servants or business associates, except that in countries which practice it, it occurs the day AFTER Christmas.