It looks to me that the DT version may be a rough transcription of the recording by MacColl and Lloyd, but MacColl/Lloyd don't have that great verse about finding Northwest. Here's a closer transcription:

PADDY WEST

Oh, as I was a-walkin' down London road
I came to Paddy West's house
He give me a feed of American hash
And he called it Liverpool scouse
He said "There's a ship that's wantin' hands
And on her you'd quickly sign
Her mate is a bastard, her bo'sun's worse
But she will suit you fine"

Take off yer dungaree jackets
And give yerselves a rest
And we'll think of them cold nor'westers
That we had at Paddy West's

Well, when I'd had a feed me boys
The wind began to blow
He sent me up in the attic
The main royal for to stow
But when I got up in the attic
No main royal could I find
So I turned around to the window
And I furled the window blind

Take off yer dungaree jackets
And give yerselves a rest
And we'll think of them cold nor'westers
That we had at Paddy West's

Now Paddy he piped "All hands on deck!"
Their stations for to man
His wife stood in the doorway
With a bucket in her hand
And Paddy sings out "Now let her rip!"
And she flung the water our way
Sayin' "Clew up your fore tl'gan'sl, boys
She's takin' in the spray"

Take off yer dungaree jackets
And give yerselves a rest
And we'll think of them cold nor'westers
That we had at Paddy West's

Now seein' we're off to the south'ard, boys
To Frisco we was bound
Old Paddy he called for a length of rope
And he layed it on the ground
And we all stepped over and back again
And he says to me that's fine
"Now when they ask if ye've been to sea
You can say you've crossed the line"

Take off yer dungaree jackets
And give yerselves a rest
And we'll think of them cold nor'westers
That we had at Paddy West's

"Now there's only one thing for you to do
Before you sail away
That's to step around the table
Where the bullock's horn there lay
And when they ask was you ever at sea
You can say ten times round the Horn
And bejesus you're a sailor since
The day that you was born"

Put on yer dungaree jacket
And walk up lookin' yer best
And tell 'em you're an old sailor man
That's come from Paddy West's

As sung by Ewan MacColl and A L Lloyd on the album "Blow Boys Blow". The tune is "Tramps And Hawkers".

source: http://www.worldnavalships.com/forums/showthread.php?p=1728465
I checked this with the MacCo../Lloyd recording - it's a good recording.