A Google search brought up 42 hits for "An Old Guitar and an Old Refrain", written in 1927 by Gus Kahn, Ben Black & Charles N Daniels (as Neil Moret), and recorded by numerous artistes. No lyrics, though, so I can't be absolutely certain it's the actual song you're looking for. An interesting post to the Forum at Seniority.co.uk from "Goodfellow" from Greater Manchester on 23rd October 2001:

"With all this reminiscing of old tunes, I wonder if anyone remembers a tune called "An old guitar and an old refrain"? I bought a job lot of records from a secondhand shop during the war, and played these records during the evening and a change from the radio, but each time I played this tune the sirens would go and off to the shelter we would go. It got so bad my Mum would threaten me with murder if I played it again. If I left it off my programme, we seemed to miss a raid. I've never heard it since but wonder if it was played as a theme tune in Afghanistan."

Joan