Now I can remember this at school in a children's songbook of traditional folksongs — only it turns out this song can be rather less polite than was thought suitable for children's ears. Like many traditional songs, it seems to exist in multiple versions. I also found the first line as "In Amsterdam …" and "In Portsmouth Town …"
Googling around I find this:
Link
That's a bit bluer than we sang at school. (It also looks like that book — does that mean all its contents? — is in copyright.) They certainly didn't have us singing, in our tender trebles,
Our songbook version used the old second person singular forms, too: "I'll go no more a roving with thee, fair maid …"We only had one night, and yet
She gave me something I won't forget
Someone at the University Bath has something similar up:
http://people.bath.ac.uk/su3bugs/songs/song/aroving.htm
But goodness knows what the status of that is. And whether the University of Bath even knows that's there and what the copyright on that text is ...
There's also a version that refers to a Nancy Dawson that turns up across the English-speaking world, including on U.S. and Australian sites. For example, it's in the University of Toronto songbook, which presumably is PD:
http://archive.org/stream/universityoftoro00martuoft/universityoftoro00martuoft_djvu.txt
Roger McGuinn has a download where he sings a version. He has some interesting material on it — it turns out that the extant versions go back to something by Lord Byron ... although he based it on a traditional Scottish song called The Jolly Beggar.
http://www.reveries.com/folkden/a_roving.html
Kind of interesting. And I suppose it would be nice to read, or even sing, traditional songs like this. I might even have a go myself, if I could (a) get the microphone steady and (b) practice a suitable seafaring voice.
But I suppose that even a very old song, if it exists in multiple versions, could only be acceptable in a version known to be in the public domain.