It is indeed in Chappell(p735) in 4 variants of at least the first verse.
He includes it in the section 'Traditional Tunes of Uncertain Date'

'If I were required to name 3 of the most popular songs among the servant maids of the present generation (c1860), I should say, from my own experience, that they are 'Cupid's Garden', 'I sow'd the seeds of love', and 'Early one morning'. I have heard 'Early one morning' sung by servants who came from Leeds, from Hereford, and from Devonshire, and by others from parts nearer to London.'

My own opinion on it, looking at all of the sets of words and the tune, it is most likely a product of the mid 18thc pleasure gardens or the theatre of that period. One only has to point out some of the terminology, damsel, Cupid, gentle shepherd, perjured, typical of those 18th century pastoral pop songs. However it has survived in several forms in oral tradition for at least 250 years and is as much a traditional song as those of the earthier sort.