Hi, Julia - This Google Search shows that the song is "Ring Down the Curtain (I Can't Sing Tonight)," and that it was recorded by Gracie Fields. Gracie recorded from the 1920's to the 1940's, with hits like "In My Little Bottom Drawer" and "What Can You Give a Nudist On His Birthday?" It looks like there is a CD of "Ring" available (click), but not in wide circulation. That's a start, though.
-Joe Offer-