Also, while obviously there are other examples of the UK's resolve to intervene militarily if necessary, Iceland can't really be called a "neutral country." It was a semi-devolved personal union of the Danish Crown. Denmark had been invaded and occupied by a hostile foreign power. Even if their king (again, also the King of Iceland) and cabinet were willing to negotiate with the Germans about the terms of occupation, it was clearly under duress. Like it or not, and despite (out of necessity) being forced to take greater control over its affairs due to the aforementioned situation in Copenhagen, Iceland was involved in the war.
If Germany thought they could coerce their new collaborationist regime in Denmark into giving them support for U-Boats out of Iceland, or even just things like weather reports, information on passing convoys, etc. they certainly would have.