This instrumental is not to be confused with the later Joe Jackson song. Also known as "Stepping Out," it was written by Memphis Slim and first released in 1959. A shade over two minutes, it features some guitar but is largely sax and piano-based. It was released on the Vee-Jay label backed by "My Gal Keeps Me Crying."
The best known recording is by Cream as a fiery guitar instrumental; the live version from the 1972 release Live Cream Volume II runs to over 13-and-a-half minutes. Its other claim to fame is that it was the partial inspiration for the Deep Purple track "Lazy," as Ritchie Blackmore pointed out in a 2017 video whimsically titled Ritchie Blackmore About His Inspiration & Thievery, although Blackmore attributed the inspiration to Clapton rather than to Memphis Slim.
Suggestion credit: Alexander Baron - London, England, for above 2