This is a Jazz song to me, very like the style he did with Chris Barber, this has good use of the horns.
But jazz is just graduated blues, innit? The breaks and chord structure are definitely blues, with a little touch of jazz. More like Jazz-Blues, a mixture.
"Slow Learner" is more like pure jazz. Probably the closest to real jazz Mark ever got. Usually, he prefers to either bluesify everything, folkify everything, or countrify.