From the civil rights movement, Guy & Candy Carawan's book "Freedom is a Constant Struggle" (Oak Publications, 1968) contains about 60 songs from the period from 1963.

Their 1963 book "We Shall Overcome" has a lot of the earlier songs.

Tom Paxton's songs from the 60's include:
The Thresher Disaster
The Great American Dream
When Morning Breaks
I read it in 'The Daily News'
There was a Time
The Willing Conscript
The Dogs of Alabama
Strange Rain
A Rumbling in the Land

Others that come to mind from the UK include:

All the Way with LBJ - Tony McCarthy 1966
Death Come Easy - Harvey Andrews
H-Bomb's Thunder
The Ballad of Jimmy Wilson - McColl/Seeger

That's a few to be going on with. A lot of the songs sung in the various protest movements of the 60's had earlier origins - sometimes just a tweak of the words, sometimes a full rewrite.

Phil