Willis was born as the son of theatre maker Dave Willis, who performed sketches in theatres in Scotland in the 1930s. Willis added many of his father's ideas to his own repertoire. In 1962, Willis had his own television show on ATV, the Denny Willis Show. In the 1970s he performed in variety in Scarborough. In 1941, Willis became father of daughter Bobbie Willis, who, just like her father and grandfather before her, became a comedian.
Willis is probably best remembered for the act "The Fox Has Left Its Lair", which he performed as Denny Willis and the Quorn Quartet, touring along various theatres in the United Kingdom and elsewhere.
"The Fox Has Left Its Lair" was written by Douglas Furber (words) and Peggy Connor (music); it was originally a novelty item performed by Jack Buchanan in the Charlot Revue of 1925. Willis changed some of the lyrics and the order of the verses to suit the act. The original lyrics are as follows:
With each new verse, repeat the previous verses and the chorus.
Alternative lines in the Denny Willis version include: