It's Robert Cinnamond of Glenavy, Co. Antrim singing Napoleon Bonaparte, which he recorded in 1955 for Sean O'Boyle who was working on behalf of the BBC.

It was issued on Caedmon TC 1164/Topic 12T 196; The Folk Songs of Britain, The Vol 8: A Soldier's Life For Me, and also on Topic 12T 269 You Rambling Boys of Pleasure.

I remember seeing the film about 40 years ago, and I recall that Pasolini used a number of tracks from TFSB.