Helmut Bickel is one of my favorite people on YouTube. He has put together literally hundreds of arrangements for both guitar and ukulele, and then created video tutorials for them. Most of them are not SCA appropriate, but a surprising number of them are, including some period songs, along with folk songs and other traditional pieces.
Don't let the fact that he speaks only in German dissuade you. Just follow the tab charts on the wall behind him, and you'll be fine. Unless you are good at memorization (I'm not), you'll want to pause each video, and copy down the tab for the songs, because he does not provide the sheet music. You can find blank ukulele manuscript paper HERE (MAKE THIS A LINK).
Scarborough Fair, an adaptation of the Simon and Garfunkel version.
Greensleeves, often attributed to Henry VIII, although it was most likely written in Elizabethan times, after Henry's reign.
The Water Is Wide, also known as Waly, Waly. It is thought that the lyrics to this traditional Scottish song date back to at least the 1600's.
Packington's Pound, a wildly popular late period tune. Sometimes attributed to lutenist Francis Cutting.