I have to say I like this as much as the original and if there was a vocal version I’d probably like it better. The Andrew Oldham Orchestra, a studio group put together by Oldham (who was the Rolling Stones original manager and producer) released five albums during the 1960s including The Rolling Stones Songbook in 1965. Also appearing on that album was a version of The Last Time, which caused decades of misery for The Verve after they sampled it for Bittersweet Symphony.
Originally the B-Side of The Last Time, Play With Fire was recorded in Los Angeles with Phil Spector (who also played bass on the track) and later appeared on the American release of their 1965 album Out Of Our Heads.
Listen to Cover to Cover on Spotify