This simple, unpretentious, jazz-oriented dance song became an international hit and earned Fabric an American Grammy award in 1963 as well as a best-selling album under the same name. "Alley Cat" also became a constant at scores of formal dance receptions such as weddings, Sweet Sixteens, Bar Mitzvahs, and others for years afterward---so much so that, within only a few years of the song's original appearance, almost nobody hearing it (or joining in the novel dance created for it) could identify who wrote and recorded the song in the first place, never mind distinguish Fabric's unadorned quartet (piano, guitar, upright bass, and percussion) from the numerous versions played at such affairs. Numerous enough that the song eventually became a kind of tacky joke as popular music tastes and attitudes changed.

That was almost unfair to Fabric, whose melodic flair and unflashy style helped him create a fine series of jazz-pop instrumental recordings in the early-to-mid 1960s (including a memorable collaboration with British clarinetist and jazz titan Mr. Acker Bilk). These included The Happy Puppy, Organ Grinder's Swing, Drunken Penguin, Never Tease Tigers, Operation Lovebirds, and Relaxing with Bent Fabric.

He later composed scores for countless Danish movies and TV series under his given name, including Matador and Olsenbanden, as well as for the Danish Royal Ballet. The 21st Century saw him make a comeback in pop music, under the stage name by which he's best known, with a dance/pop project that leaned in part on modernising many of his earlier songs including "The Alley Cat." The title track from the project, Jukebox, became a hit in his native Denmark, a chart-topper in Japan, and a sleeper hit in the United States; its title track was used in a Coca Cola campaign in Germany and now used on ten different soundtracks for American movies.