"I Am A Jolly Foster" is a traditional English folk song. Written in 4/4 time, it dates from at least the time of Henry VIII, and a version of it can be found in Music At The Court of Henry VIII, Transcribed And Edited By John Stevens, Second, Revised Edition, published by Stainer And Bell, London, (1973). It is quite likely that Henry played the song himself, although it probably predates him.
Far from a popular traditional song, it has nonetheless been recorded in the 21st Century.
A "Foster" was the title given to an administrator of hunting territories that belonged either to the king or to a bishop. At one time, England was well forested, and even wild boar could be found there. Although the office of foster has gone the same way as many other ancient professions, the word lives on as a surname, e.g. as in "Foster's Mill."
Suggestion credit: Alexander Baron - London, England, for above 2