Apparently, Bert's tune for Tam Lin is derived from one from relatively recent oral tradition. Amazingly,in the 60s, 2 fragments of this ballad (which was previously only known from print) were found in the repertoires of 2 Scotish travellers - Betsy Johnson and Willy Whyte. Both of these fragments are to be heard on the CD 'The Muckle Sangs' (Greentrax Records, CDTRAX 9005). Off the top of my head I can't remember which one Bert based his tune on - when I've got a bit more time I'll play it again and let you know.
I heard Bert sing his version of this ballad, at Peterborough Folk Club c. 1968. This is a treasured memory - he really was an amazing singer!