Moonlight Serenade

"Moonlight Serenade" was a song by Glenn Miller.

DJ played it when he met Peri in Tranquil Repose. (TV: Revelation of the Daleks)

Jack Harkness played while he was discussing "business" with Rose Tyler, whom he believed to be a Time Agent. (TV: The Empty Child) Later, the song was playing on the radio when Rose and the Ninth Doctor were trapped in the storeroom of a hospital; Rose attempted to dance to Moonlight Serenade with the Doctor. The Ninth Doctor had Moonlight Serenade playing in his TARDIS console room when he rescued Jack Harkness from the explosion on Jack's Chula warship. (TV: The Doctor Dances)

Behind the scenes
In the real world, "Moonlight Serenade" was released on 1943, two years after the setting of The Empty Child.