The Roud index lists about 110 songs collected in Staffordshire, but I don't know if they are from the north or south of the county. By far the most important contributor of Staffordshire songs was George Dunn and I am sure you can find recordings of him. Nutty mentioned Jon Raven who of course did a lot of work on songs of the Black Country and then there's Roy Palmer who did some collecting in the area. Sharp and Gardiner both noted songs in the county, and there's a number of children's songs from the late C19.

Most of the collected songs seem to be versions of songs noted all over the UK, but there is one called "Quarry Bank Mashers", in Roy Palmer's book "Everyman's book of English Country Songs."

Hope that helps.

Gwilym