As far as I know they're two different persons: the bandleader Johnny Spence, who had a U.K. hit with his orchestra with the instrumental Theme from Dr Kildare in 1962 (I guess he's the one you're referring to), and the bassist Johnny Spence, who played with U.K. rock band Johnny Kidd & the Pirates; they had a couple of U.K. hits in 1960 and again in 1963.
I can't find any info on the bandleader.