I checked with Dennis Cook, who sings this song (and from whom you heard it the other weekend).

The song is The River Lea from Joanna C. Colcord's Songs of American Sailormen, p. 181, although the tune he uses is not the one in Colcord's book, but rather, learned from [a tape by] Jim Douglas. The words transcribed from Colcord follow:

THE RIVER LEA

It was one fine day in the month of May,
And I was outward bound.
I hadn't any tin to buy some gin,
So I walked the street all around.
My shoes was out at the elbows,
And I was sore in need
So I shipped as a jolly sailor
On board of the River Lea.

No more I'll go to sea,
beat down the bay of Fundy.
Forever more I'll stay on shore,
I'll go to sea no more.

No more I'll take my first lookout
No more I'll take my wheel.
No more at the cry up aloft I fly,
While "Ay, ay, sir!" I squeal.
No more I'll reef those topsails,
For it is no more my trade.
No more I'll brail that spanker in
On board of the River Lea.

No more I'll pull on the lee fore brace
Nor by royal halliards stand,
No more I'll ride those swifters down
With a tar-pot in my hand.
No more I'll cross those royal yards
Nor furl that flying jib.
No more I'll shift gaff-topsail tacks
On board of the River Lea.

I've crossed the Western Ocean,
I've sailed the raging main
But I've made it a rule that I won't be a fool
And go to sea again.
I'll stay at home in comfort
And good advice I'll give:
Don;t ever ship as a sailor
On board of the River Lea.
^^
Colcord's notes:

The next song was composed by a contemporary shantyman, named Sam Peck. Like all songs of this nature, it goes back for its inspiration to one still earlier--the adventures of poor Ben Brace, who was robbed of his clothes by a San Francisco lady named Angelina, and had to ship out on an Arctic whaler. Unlike the original, Mr. Peck's song is quite fit to print! The original song, portions of which Mackenzie gives under the title "Dixie Brown," is frequently confused with "Greenland Fishery," (page 151 [in Colcord]) but I think there is no connection between the two.

--Charlie Baum