You could look at the medieval Scottish tune "Gilderoy" which, in twists and turns has formed the basis of later variations such as the tune used for "Dives and Lazarus" and "The Star of the County Down", etc. Just one example.

The other interesting fact (to me, at any rate) is the way in which comparatively modern tunes with known composers - such as Tom Anderson, Andy Cutting or John Kirkpatrick - can slip seamlessly into "traditional" music sessions.