This song is an update of the 1950 Muddy Waters blues classic "Rollin' and Tumblin'" and nominally a tribute to the bluesman. As well as the four Yardbirds members, the track also featured The Rolling Stones' Ian "Stu" Stewart on piano.
This was a track on Little Games. The album was produced by successful singles producer Mickie Most, who was brought in by The Yardbirds' record company to coax out more commercial product. Although Page had worked earlier for Most as a session guitarist, he was unhappy with him taking on the production duties as the producer was basically interested in singles and didn't believe it was worth spending much time on album tracks. Page recalled to Mojo magazine July 2014. "You'd finish recording the track and Mickie would just go 'Next!'"
"I remember that happening during 'Drinking Muddy Water,'" Page continued. "Stu looked at me and he said 'I can't believe this! I've never worked like this in my life! And I said to him, 'And you're not going to start now! We're going to hear a playback. And we did, but everything was based around the idea of getting things done quickly."