Political map of the Arctic & the Far North 10 May 1940 (Invasion of Iceland): When the Danish government capitulated (German invasion of Denmark (1940)), Iceland assumed full control over its own affairs. Despite this, and Icelandic insistence on neutrality, the British still feared the possibility of Germany extending its influence over the island and invaded in May (Invasion of Iceland). The local authorities offered no resistance, reluctantly agreeing to cooperate with the Allies (Allies of World War II) for the rest of the War (World War II).