I can remember that being on the radio often around 1960 along with Smoke Gets In Your Eyes. (If you are old enough you will remember the Esso Blue advert as well) That was considered rather daring and cutting edge stuff by the BBC in those days. Thank heaven the Beatles and then pirate radio stations came along in 1963 and 1964 to open up a whole new world to us young teenagers.
Not quite old enough to remember hearing it on the radio in 1960. The Rolling Stones introduced me to authentic blues music. I'm not sure the BBC was ever cutting edge.