I was mistaken: the song is untitled in the book. Normally in a book, you'll find page headings which give the book name on the left and the chapter or section heading on the right. But in this book, the left and right headings together form a short descriptor for that pair of pages. The descriptor for this pair is "The first / drinking song". [Note: each verse in this song is preceded by a Roman numeral.]

This descriptor implies that there are other drinking songs in the book, and that is indeed the case. You will also find (ignoring very short verses and fragments):

pp.92-95: Song of the Pelagian Heresy for the Strengthening of Men's Backs...
Descriptor: The drinking song / of Pelagius
First lines: Pelagius lived in Kardanoel / And taught a doctrine there
with score and narrative interpolations

pp.112-4: Descriptor: The song called "His Hide / Is Covered with Hair"
First line: The dog is a faithful, intelligent friend
with score and interpolations; incomplete

pp. 129-31: untitled. Descriptor: And a threnody / is chaunted
First line: Attend, my gentle brethren of the World
With interpolations. This song is described as having "a sort of dirge" rather than a tune.

pp. 156-57: Descriptor: The rhyme of / lucky burial-days
First line of eight: Buried on Monday, buried for health
Called first an "old rhyme", later a song.

pp. 171, 173: Descriptor: The great war between / Sussex and Kent
First lines: If Bonaparte / Shud zummon d'Eart / To land on Pevensey Level (one verse only)
Tune: Golier (score given)

pp. 208-9: Descriptor: His own country (on each page)
First line: I will go without companions

p. 243: The Sailor
First lines: Noël! Noël! Noël! Noël! / A Catholic tale have I to tell:
Descriptor: The Sailor's Carol; three stanzas, with score

pp. 262-3: Descriptor: Song of Duke William
First line: Duke William was a wench's son

p. 286: Golier. See score on p. 171.
The song appears to consist of only three lines:
And I will sing Golier!
Golier, Golier, Golier, Golier,
And I will sing Golier!

pp. 287-8: Descriptor: The Californy song; with score
First lines: I am sailing for America / That far foreign strand

pp. 289-92: Descriptor: The last song
First line: Thou ugly, lowering, treacherous Quean

pp. 307-10: Descriptor: A piece of verse / is written and / I come to my home
First line: ... and therefore even youth that dies

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Did Belloc supply scores in other books?