There were a number of songs composed about the Jarrow Marchers there is at least one songster of them. Alan Price was famous for his but that wa more recent than the march and it was a pop song. The march took place in 1936
Many wrote songs for March commemorations. Try a google search for those.
The Whiskey Priests (great band from the N.E.) had a Jarrow Song on their CD Timeless Street.

Outside of that no songs it seems contempoary with the march about it.

Conrad