The Amazon.com MP3 Store has an audio clip of "Midnight In Moscow" by Kenny Ball And His Jazzmen on the album listed below. Click on the album name and you will be taken to a list of mp3 album tracks with audio samples that include the above song.
The Pye Jazz Anthology - Kenny Ball And His JazzmenCDUniverse also has a clip of the above song on the album listed below. Click on the album name and you will be taken to a list of albums, including the one below, that include the above song. (Note: Those albums with music note icons all have song clips. To see the entire list of CDs, you may need to scroll down all the way to the bottom as many songs have lyrics and other information displayed at the top.)
Billboard Top Pop Hits 1962 - Various Artists