Just to complete the picture the query in 1967 in English Dance and Song
was answered in the following 3 editions with similar information already given above with no light thrown on the identity of A. T.

The earliest date given above, 1851, I can't push further back and can only add as far as broadsides go all of the printed broadsides I have are of that same mid-19th century period. The only one dated precisely is by The Glasgow Poet's Box at 1866.

Checking Kilgarriff for A. T. throws up only 2 possibilities. An A. Trail has a single entry of 1865 'You needna come courting o' me' music by W. T. Wrighton. The other is the already mentioned Arthur Tennyson who does interestingly have an entry for c1865 with 'All along the Valley' (music by Claribel), a parody of his own work? Probably not but a strange co-incidence all the same.