Here is what I came up with...
Looking at the Grommit reference photos, I think your clay looks far too wet and shiny.
In the material I came with I used: a glossiness value of around 0.3, Used both a bump and displacement, and some noise in the diffuse mixed with the colour to provide some subtle colour variation.
For the bump map... I 50% mixed two versions of the fingerprint map that davemahi provided, one with a strong blur and an unmodified version.
I then used a heavily blurred grungy looking map, with a 4mm spread in displacement.