From the long, long, LONG-running BBC show, Doctor Who. The Doctor (Sylvester McCoy) and companion Bonnie Langford (Mel Bush) win a trip to the British Shangri-La Vacation Camp in the year 1959 in the three part episode "Delta and the Bannermen" (2, 9, and 16 Nov. 1987).
This band plays the music for the camp dances. Its real reason for existing was to save the BBC a few quid by covering some '50s tunes to avoid paying for the original versions. It was made up of some studio musicians and singing duo The Wilson Sisters.
The episode was written by Malcolm Kohll.