The song appeared in The Penguin Book of English Folk Songs (1959), which would be the ultimate source for most if not all revival sets. H.E.D. Hammond noted it from Mrs. Marina Russell of Upwey, Dorset, in 1907; to begin with, he thought that she had sung Mourners, and he printed the song as such in The Journal of the Folk Song Society, vol.III issue 11, 1907. Frank Kidson pointed out that another version, entitled A Jug of This, noted in Wiltshire in 1857 and having a different tune, had appeared in Barrett's English Folk-Songs (1891); it was clear from that that the word should be Mariners. Hammond agreed, noting that mar'ners appeared in Hardy's The Mayor of Casterbridge as a dialectal form of mariners.

It's hardly surprising that it's hard to find the song in the DT if you don't know some of all that!

Mrs. Russell had a fine memory for tunes, but was apt to forget the words; so that the set Hammond published was in fact her tune with almost all of the text coming from another variant noted from W. Haines of Halfway House, between Yeoville and Sherbourne. He sang it to a tune related to Mrs. Russell's, but in the major.

The song appeared on broadsides of the 19th century; examples can be seen at Bodleian Library Broadside Ballads, including:

Jug of this ("You tiplers all as you pass by ...")  Printed between 1819 and 1844 by J. Pitts, 6, Great st Andrew street, 7 Dials [London].