I refer you to that excellent article 'And They Calls I Buttercup Joe' published in the 2006 Folk Music Journal which states:

"The provenance of 'Farmer's Boy' is generally unknown, but appears to be the work of Suffolk poet Robert Bloomfield (1766-1823), although Rod Stradling suggests that the tune is 'Ye Sons of Albion' which dates back to the Napoleonic Wars ..."

This information was found in "Sussex Songs, No. 9 – The Farmer's Boy', Sussex County Magazine, 4 (1930), 988–89. The same article gives a version of the song by Albert Handley of Hastings, who 'has also written some additional verses'."