In Chappell, "Popular Music of the Olden Time," vol. 2, Notes to the song "Old Sir Simon the King":

In "Hans Beer-pot, his invisible Comedie of See me and see me not (4to., 1618), Cornelius says that gentlemen did not formerly avow drunkenness, but "now beggars say they are drunk like gentlemen." He adds that he has heard "an old fantastique rime:"
"Gentlemen are sicke, and Parsons ill at ease,
But serving men are drunke, and all have one disease."

These lines are a paraphrase of the two following in "Old Sir Simon:"-
My hostess was sick of the mumps, the maid was ill at ease,
The tapster was drunk in his dumps; they were all of one disease."

Again in "The famous Historieof Fryer Bacon:"-
"Lawyers they are sicke, and Fryers are ill at ease,
But por men they are drunke, and all is one disease."

"I am informed by Mr. Payne Collier that Fryer Bacon was printed soon after 1580,.... and these quotations increase the probability of Ritson's conjecture that the "hey, ding a ding," mentioned in Laneham's Letter [from Kennelworth] in 1575, was Old Sir Simon."
Chappell continues with other versions, mentioning "Sportive Wit, The Muses' Merriment," 1656, where the burden is quoted in a medley of songs:-
"Old Sir Simon the King
With a thread-bare coat and a malmsey nose,
Sing heigh---"

From vol 1, p. 262-269, with several versions and music- Chappell says the tune is contained in Playford's "Musick's Recreation on the Lyre Viol, 1652.
Other songs were based on Old Simon, including "Ragged and torn, and true; or 'The Poor Man's Resolution," and "The Reformed Drinker" and the "Grist Ground at Last...." given above by IanC.