Since 1977 several groups and individuals have circumnavigated Iceland by kayak. Here is what I believe to be a complete list, with some references and links. Please let me know if you are aware of others!
1977 Nigel and Geoff. You can read Nigel's account of part of their trip in the book Raging Rivers Stormy Seas by Storry, Bailie and Foster, cover shown below.
1986 John Bauman with the man he names only as Harry in his story of the journey, told as Icelandic Odyssey, in the book Seekers of the Horizon, a compilation of sea kayaking trips edited by Will Nordby 1989, cover below. Harry wrote about that trip for the fall 1988 issue of Sea Kayaker magazine in an article titled "Icelandic Saga"
2003 Chris Duff, Shawna Franklin and Leon Somme.
2006 Rotem Ron completed the trip solo.
2007 Freya Hoffmeister and Greg Stamer.
2009 Gisli Frdgeirsson, an Icelander, solo
2009 Margaret Mann, solo
2011 Riaan Manser and Dan Skinstad on a tandem kayak
Raging Rivers Stormy Seas
Seekers of the Horizon