I play it with just Dm and C with fills doing the rest. That is, the Fairport-styley version as opposed to the Nic Jones/ Martin Simpson Little Musgrave arrangement.
I'm pretty sure Simon Nichol plays it with only these two chords, (I think he uses Am and G capo'd on the 5th fret if memory serves).
when I saw Fairport (Acoustic) Convention in Kendal a few years back he introduced it as follows:
"This song has two chords and 19 verses which makes it a folk song, whereas if it had two verses and 19 chords that would make it a Steely Dan song".