KH suggests that Iceland did not play a really significant role in World War II.
I think that Iceland’s role was highly significant, especially for a population of less than 300,000.
The anchorage in Hvalfjörður supplemented and eventually largely replaced Scapa Flow in the Orkneys as a base for the warships guarding against operations by German heavy ships into the Atlantic to threaten the convoys essential to keep Britain in the war and support the reconquest of continental Europe.
Icelandic airfields were essential to the buildup of American airpower in Britain. They were essential to the operations of the long-range patrol aircraft (mainly B-24s) which covered the central Atlantic and prevented the German U-boats from organizing their wolf-packs around the convoys. I don’t think it’s a coincidence that Keflavík became operational in March 1943 and the Germans broke off the Battle of the Atlantic in June due to intolerable U-boat losses. Reykjavík airfield was useful but had limitations.
British fishermen were mostly unable to operate in World War II. Icelandic fishermen carried on despite appreciable losses inflicted by U-boats and German aircraft, and supplied a significant amount of Britain’s food during the war.
As a matter of interest, in 1940 the German armed forces estimated that while they could probably seize Iceland, they could not hold it.
Douglas Woodard, St. Catharines, Ontario, Canada