Several tunes. See thread 24291: Sweet William
There are two in the DT. The first (Wagon Lad) is the same as the first in Numachi, and the other is like the second in Numachi.

The tune in Sam Henry's "Songs of the People" differs from both. Most versions drop one or another of the verses to make six, but Henry printed all seven. There is surprisingly little difference in the lines so I would guess that all are based on the lyrics in Buckstone and Fitzwilliam. Henry "sees lambkins at play," Contemplator and #1Peasant hear "nightingales."
Henry's order is:
As I went a-walking
Why are you loitering here,
Oh, I will buy you fine beavers
Oh, I want none of your beavers
Come let us be going, kind sir,
When he came there and saw she was gone
I'll do as the schoolboy, spend my time at play.