But, here's an interesting article from American Music suggesting that's probably not true (and, therefore, I didn't "know" it for all you epistemologists playing along at home).
Let’s begin with the basic historical question. What proof is there, that the British at Yorktown played a march that anyone living in the eighteenth-century called ["The World Turned Upside Down", hereafter] WTUD? The Yorktown/WTUD story was first published in Major Alexander Garden’s Anecdotes of the American Revolution . . . (Charleston, S. C., 1828), forty-seven years after Yorktown. Garden quoted a letter from Major William Jackson who described the surrender negotiations as though he had been an eyewitness, but didn’t mention that he was in Europe, not Yorktown at the time.But, don't let all that stop you from singing along heartily with the English Civil War royalist version (revived by modern Jacobite sympathisers):
Apparently, in that same letter, Jackson also stated that a French fleet had sailed from Brest for America early in May 1781 at the instigation of his superior officer, Lt. Col. John Laurens. That French fleet was crucial to the victory at Yorktown, but Laurens was in no way responsible for getting it to America. In fact, that French fleet had sailed late in March before Laurens and his secretary, Major Jackson, arrived at Versailles. This shows that Jackson cannot be trusted for details of past events in which he was closely involved, much less for details of something that allegedly happened at Yorktown while he was 3,000 miles away in Europe.
...As published, Jackson’s Yorktown/WTUD story is, at best, a dubious “third-hand account”—Laurens(?) to Jackson to Garden—masquerading as an eyewitness report.
This Yorktown/WTUD story had been ignored for a long time. ... Then in 1881, Henry P. Johnston revived the Yorktown/WTUD story from Garden’s book (with credit), for his excellent Yorktown Campaign and the Surrender of Cornwallis... Around that time a few people began to ask about the music so that search has been going on for just over a century.
The first to write that he might have found the WTUD music was John Tasker Howard, a music historian who about 1931 wrote a booklet, The Music of George Washington’s Time for the Bicentennial of Washington’s birth. Howard was a fine scholar who knew a great deal about American classical music and a lot about Stephen Foster’s songs but not much about the other songs of ordinary people and next to nothing about fife and drum music. (This last point is important. The surrender terms specified that the surrendering troops could beat British or German airs. “Beat” applies only to drums.)
John Tasker Howard learned that a 1642 English Royalist tune, “When the King Enjoys His Own Again” had once had a song text called “The World Turned Upside Down” associated with it (in 1646). He then suggested that this “King Enjoys” tune might also be the as yet undiscovered WTUD music. Howard didn’t know that WTUD text in no way fitted Yorktown.
Unfortunately for Howard’s guesswork, there is only one known period copy of that 1646 WTUD text; no evidence that it ever was sung; and no sign of any later reprint until 1923 when it appeared in Hyder Rollins's Cavalier and Puritan: Ballads and Broadsides Illustrating the Period of the Great Rebellion, 1640–1660! ...though Howard was tentative in his notes, his published music copy appeared with a bold face “The World Turned Upside Down” title in his booklet. The result is that unless you read Howard’s text carefully you can easily come away with the false notion that the “King Enjoys” music has been proved to be the WTUD music. In fact, the “King Enjoys” music was never known as WTUD until Howard published it that way in 1932!