They did indeed - here's a page about Music While You Work, with a sound file of the theme music, for the last show, in 1967:

"From June 1940 this long-running series broadcast two live bands a day to British factory workers to increase wartime productivity and morale. By the end of the war 5 million workers in over 9000 factories were tuning in.

The programme continued after the war but by 1967 it seemed outdated and ceased when the Light Programme became Radios 1 and 2."