From Wikipedia:

" 'The Lambeth Walk' is a song from the 1937 musical Me and My Girl (with book and lyrics by Douglas Furber and L. Arthur Rose and music by Noel Gay). The song takes its name from a local street once notable for its street market and working class culture in Lambeth, an area of London, England.

"The tune gave its name to a Cockney dance first made popular in 1937 by Lupino Lane. The story line of the original show concerns a Cockney barrow boy who inherits an earldom but almost loses his Lambeth girlfriend."

The article goes on to say that the song gave rise to a dance fad that was roundly condemned by the Nazis, which I suppose is a good enough reason to sing it and dance it.