Kennedy's reference to Ashton's "Real Sailor's Songs" will probably be to "Polly Dear, Now I MUst Leave You" pp65-66 (John Foreman's 1973 reprint) which goes:

Polly dear, now I must leave you,
For to cross the ragiung main.
I am afraid my absence will grieve you
For losing of your darling swain;
Hark, hark, how the seas do call me,
I'll no more grieve at my Polly
Still I'm in hopes to please my Polly
When from the seas I do return.

Billy dear, when you are landed
In some other foreign part,
Some other girl you may be seeking,
You'll never think on your seetheart.
O, my dear you may believe me,
And so kindly may receive me,
Polly dear, you need not doubt me,
You are the girl I do adore.

Seven long years and something better,
Before young William came on shore,
He was drest like some shipwrecked fellow,
He seem'd to be very poor.
Then he came to see his Polly,
Drest like some shipwrecked fellow,
It was only to try his Polly,
Whether she loved him or no.

As soon as she beheld his features,
Then she fainted quite away,
But, when she came to herself again,
These very words to him did say.
O, Billy dear, you may believe me,
Broken hearted you have made me,
Broken hearted you have made me,
You are the lad I do adore.

(A bit confused I venture!)