Lesley has accepted uncritically, and précied, comments made by William Chappell back in 1859. Chappell confused two distinct songs, as did many others in the early days of folk song scholarship. In fact, it is 'The Sprig of Thyme' that is sometimes attributed to Mrs Fleetwood Habergham, not 'The Seeds of Love'. She is supposed to have written it as a sort of lament for her husband's disgraceful behaviour.

The songs are similar, and the latter was probably based on the former, often sharing lines or whole verses with it (though the particular line you mention seems to belong only to 'Seeds') but it doesn't appear prior to the broadside printing by Pitts of London in the early 19th century. 'Sprig' is considerably older; the original appears not to have survived, but there is an 'answer' to it on a broadside of 1696.

As it happens, there is a useful summary of the history of 'The Sprig of Thyme' in the revised edition of Frank Purslow's book Marrow Bones, which will be available from EFDSS in a few days' time. There appears to be no evidence that either song ever had any Jacobite connection, nor has that ever been suggested by anyone so far as I know.