Menyanthes trifoliata; The Bogbean is a plant that can not be mistaken. It grows in (very) wet places often in water like ponds and lake margins. It can be found in most regions on Iceland where these conditions occur. Obviously it is not a plant of the rugged highlands but rather more so of the coastal fringe of Iceland. It should be noted though that it can not resist salty conditions. Wherever you see a sturdy waterplant (very thick leaf stalks/petioles) with a trifoliate leaf and white flowers (buds often red) on a flower stalk, you can be shure it is the Bogbean.
It is a member of the Bogbean family: Menyanthaceae.