The band formed in August 1983 when Ásmundur Jónsson from Gramm Records wanted to create an avant-garde supergroup to perform on the final episode of a radio show called Áfangar.

Einar Örn had studied media at the Polytechnic of Central London, which enabled him to come in contact with UK anarcho-punk groups such as Flux of Pink Indians and Crass.

Later that year, Kukl and Icelandic folk singer Megas (Magnús Þór Jónsson) formed a side project called Megakukl.

Guðlaugur and Björk formed the Elgar Sisters, a group which featured musicians from Kukl (with the exception of Einar Ørn) and collaborators Hilmar Örn Hilmarsson and Þorsteinn Magnússon.

In the summer of 1986, Einar Ørn returned from England with two projects: the creation of a new record label, Smekkleysa/Bad Taste, and a new band, Sykurmolarnir, later translated as The Sugarcubes.

Björk, Einar Örn, Melax and Sigtryggur formed the Sugarcubes in 1986 with bassist Bragi Ólafsson and guitarist Friðrik Erlingsson (replaced by Þór Eldon).

As a polytechnic engineer in practice and inventor, he has also combined his music work with scientific projects and delved into quantum physics, thermoelectricity and navigational systems.