Very much the same tune is in the Thomas Watts MS from the Peak District, but there it's listed as 'The Turk's March, by Handel'. Googling this title gets you nowhere, and Handel's Gavotte in G major isn't the one, either. Handel wrote another gavotte in Bb, but although that isn't 'Sir Sid's', it bears a resemblance to 'Jack the Horse Courser's Hornpipe' as recorded by Harry Boardman.

I'd be interested to see if anyone comes up with anything on that Handel link.