"Sussex Drinking Song," originally titled simply "Drinking Song" was published in Belloc's The Four Men: A Farrago (1912), pp. 86-7; online/downloadable copies at Internet Archive.

The original words differ from what has been presented above. For instance, the poem begins:
"On Sussex hills where I was bred,
When lanes in autumn rains are red, ...

In the book you will also find Belloc's own score for a melody.
An ABC transcription:

X:1
T:Drinking Song
C:Hilaire Belloc
M:6/8
L:1/8
K:F
c|F2F F2G|A2A A2F|A2G A2B|c2c c2c|d2d f2d|1 c2A F2G|Acc (cB)A|G3 z3 :|
|2 c2A F2A|GGF F2G|F2G A2F|G2A B2G|A2B Hc2A| GFF F2F|F3 F3|]

To play or display ABC tunes, try concertina.net

At Google Books, the poem is included in the miscellany A Tankard of Ale (1920).

There has been at least one previous thread discussing both this song and Belloc's "West Sussex Drinking Song".