Perhaps I shouldn't be answering my own question, but...

From Raoul F. Camus, Military Music of the American Revolution (Chapel Hill, Univ. of North Carolina Press, 1976) pg. 163:

Alexander garden wrote in 1828 that "the British army marched out with the colours cased, and the drums beating a British or German march. The march they chose was - The World Turned Upside Down" Many writers have since referred to this tune, skilfully embroidering the legend. The fact is, however, that the song was not recognized by the majority, if any, of the witnesses, for none of the contemporary journals located to date deemed it worth of mention.

Camus goes on to enumerate contemporary sources that mention no specific music at all. He quotes several which do make general reference to the sort of airs and cadences that were heard by those in attendance. But his conclusion is that, "the sole source of the legend seems to be the anecdote written by Garden in 1828." [i.e. two generations after the event - GW]

I'd recommend Camus as a starting point to anyone interested in pursuing this.

He does conclude that IF Garden had a witness who did hear something which he or she identified as TWTUD, that something might have been "When the King Enjoys His Own Again". Units present would have known it, and it was suitable for a slow march.

But hey, its folklore! -George ::-.--O