Just looked up A-Rovin' in Stan Hugill's Shanties from the Seven Seas. It gives under version (d), the additional verse:

In Number One New England Square,
Me Nancy Dawson she lives there.

Not Faithless Nancy Dawson, but close.

His verse 20 in version (a) is:

Now when I got back from sea,
A soger had her on his knee.

Which is certainly faithless!