Doing some digging around on Bjork's pre-Sugarcubes work, we came up with a few more video gems:

Tappi Tikarrass performing live in 1982

Tappi Tikarrass was founded after her all-girl punk band Spit and Snot, and were often compared to early Siuoxsie and the Banshees and The Cure. It was KUKL though which really fleshed out a distinctive post-punk sound. Their first live show was in Reykjavik in September 1983, opening for Crass, who released KUKL's first album The Eye in 1984, based on the book Story of the Eye by Georges Bataille.

Live clip,music video for 'Anna' and the infamous pregnant performance from Icelandic television.