This is from the memoirs of Kenneth Baker, chairman of the Conservative Party in the last days of Margaret Thatcher:
'My first real memories stem from that time, and the outbreak of war. The radio was crucially important, and I remember hearing tunes like Run, Rabbit, Run, Who Do You Think You're Kidding, Mr Hitler? and Hang Out the Washing on the Siegried Line.' - Kenneth Baker, The Turbulent Years (Faber & Faber, 1993) pp.4-5
Well, probably not. Who Do You Think You Are Kidding, Mr Hitler? was written in 1968 by Jimmy Perry as the theme song to Dad's Army.