Versions in the DT are (the second is what is asked for):

OVER THE HILLS AND FAR AWAY (John Gay) (from Beggar's Opera)

OVER THE HILLS AND FAR AWAY (2)

OVER THE HILLS AND FAR AWAY (4) (From Pills to Purge Melancholy)

OVER THE HILLS AND FAR AWAY (OHIO, 4) (Another version of The Wind it Blew my Plaid Awa'; From the French and Indian War)

SO EARLY IN THE MORNING (From The Irish Songbook, Clancy Bros. & Tommy Makem)

One of the discussions in the Forum is:

'O'er the Hills and Far Away'

See the Pills to Purge Melancholy (1706) version: The Recruiting Officer: Or, the Merry Volunteers (from Bruce Olson's site). This is probably the original you are asking for.

Martin Carthy's versions (from Garry Gillard's site) are:

(1) Over The Hills And Far Away ("Hark now the drums they beat again")

(2) Over The Hills And Far Away ("Tom he was a piper's son")

~Masato