I bought a video of Martin teaching his method. His usual tuning is CGCDGA. The songs you have quoted are very early ones and he might have been using something closer to standard way back then or possibly DADGAD. Suffice to say that his current tuning requires radical rethinking about how to play the instrument. The video is called "Martin Carthy - British Fingerstyle Guitar". The catalogue number is OV11208 and is distributed by Music Sales Ltd, Newmarket Road, Bury St. Edmunds, Suffolk, UK IP33 3YB

I'll have a pint of Greene King Triumph please.