"The Dransfields played on the original Sandy Denny recording of the song"

That would be Sandy's The North Star Grassman and The Ravens which featured:

Sandy Denny, vocals, piano, acoustic guitar;
Jerry Donahue, electric guitar;
Richard Thompson, 12-string, electric and acoustic guitar, bass, accordion, vocals;
Trevor Lucas, acoustic guitar, backing vocals;
Buddy Emmons, pedal steel guitar;
Pat Donaldson, Tony Reeves, bass;
Gerry Conway, Roger Powell, drums;
Ian Whiteman, piano, flute organ;
Barry Dransfield, violin, backing vocals;
Royston Wood, Robin Dransfield, backing vocals;
Strings arranged by Harry Robinson

Charlotte (had to check her copy of the record)