I found it on the DVD - it's right at the end of Chapter 11 of the DVD. The tune used in the movie is The Bonny Ship the Diamond. What I hear on the movie is:

Come all you bold young thoughtless men, a warning take by me
And never leave your happy homes to sail the raging sea

Here's my transcription of the lyrics from Harding B 25(294), one of the broadsides Malcolm linked to above.
-Joe Offer-

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The British Tars

Come all you thoughtless young men,
A warning take by me
And never [leave] your happy homes
To sail the raging seas
For I have ploughed the raging main
This twenty years and more
But now I am turned adrift to starve
Upon my native shore.

When war at first assailed us,
I quickly left my trade,
Our country was in danger,
I flew to lend my aid,
And in my country's service,
Long, long fatigues I bore
But now I'm turned adrift to starve
Upon my native shore.

By storms and raging tempests
Shipwrecked three times I've been
And many a bloody battle
Upon the seas I have seen.
I've seen the cannon's glaring flash
Have heard its murd'rous roar
Tho' now I'm turned adrift to starve
Upon my native shore.

The British Seaman's valour
To all the world is known
We conquer still where e'er we go
The action is our own.
The Metor (sic - perhaps Meteor) flag of Haughty Gaul
Triumphantly we bore
But now we are turned adrift to starve
Upon my native shore.

Should hostile fleets e'er venture
Upon the raging main
True Hearts of Oak we British Tars
We'll push to sea again.
And bravely bring their ships to port
As we have done before.
So help us now while we are in want
Upon our native shore.

Come pity ye gentle stranger
A luckless British tar,
In your defence you yet may hurl
The thunder bolt of war
Come lend me some kind assistance
And heaven will bless your store
For now I'm turned adrift to starve
Upon my native shore.