Well, there are plenty of resources to look at here.  Here are some:

The Bodleian Library in Oxford (UK) has a large collection of broadside ballads -that is to say, songs that were printed and sold cheaply by travelling salesmen, up until the early years of the 20th. century.  If you click on these links, you'll see some versions of "Henry Martin":

Henry Martin  Printed between 1820 and 1824 for W. Armstrong of Liverpool.
Henry Martin  Printed between 1845 and 1859 by Ryal & Co., Printers, 2 & 3, Monmouth Court, Seven Dials, London.

There are quite a few more, but these ones have dates, so are probably more useful to you.

There is an entry at  The Traditional Ballad Index:

Henry Martyn [Child 250]  -You may find it a bit confusing, but what it really says is that nobody can be quite sure who wrote the song, or when.  It also makes the point that old songs often get changed quite a lot, and finish up with different titles; "Henry Martin" is also known, for example, as "(Sir) Andrew Barton" (and lots of other names, too) -people in those days usually learned songs just by hearing other people sing them, and so they would quite often get muddled about some of the words.

These songs aren't just old and forgotten, though; people still sing them.  There's a very interesting website, for example, called  The Max Hunter Folksong Collection,  where you can hear a recording of a traditional version of "Henry Martin" (though it's called "Andrew Batan", it's really the same song) sung by someone in Arkansas in 1958.  That will sound like a long time ago to you, but I was four years old that year, so it isn't really such a long time, honest!

I wish that I'd had such an interesting project to do when I was at school.  I hope that I've told you enough, but if I haven't, please say so; there's lots more.

With best wishes

Malcolm