Behind the scenes Edit
Like Clara, many people in the UK often refer to the music as "The Benny Hill Theme", due to its use as the theme tune for The Benny Hill Show. In reality, the piece is titled "Yakety Sax" and was first performed by American saxophone player Boots Randolph (the song's co-composer) in 1963.
The fact Clara is able to overdub the music over a video implies her phone has an app to do this. Although no such app exists (yet) in the real world, there are websites such as "Benny Hillifier" that will add the music to streaming videos. However Clara's computer skills were artificially increased in TV: The Bells of Saint John, thus giving her the potential to do this on her own.
The theme is typically used in fast-forwarded scenes with odd antics.