Rockall is a territory of United Kingdom
The important section of the Act was this: "As from the date of the passing of this Act, the Island of Rockall (of which possession was formally taken in the name of Her Majesty on 18 September 1955 in pursuance of a Royal Warrant dated 14 September 1955 addressed to the Captain of Her Majesty’s Ship Vidal) shall be incorporated into that part of the United Kingdom known as Scotland and shall form part of the District of Harris in the County of Inverness and the Law of Scotland shall apply accordingly." [...] In terms of proximity there is little doubt that Rockall is Scottish. The nearest point of Scotland to Rockall is Soay in the St Kilda archipelago which is some 187 miles, 301km, to the east. The nearest point of Ireland, which now does not actually have a formal claim to Rockall but which argues that it cannot be used to determine territorial rights, is Tory Island, some 263 miles, 432km, to the south-east of Rockall. [...] Ten years later, Ireland was still arguing about Rockall, and the Westminster Parliament was still debating. Sir John Biggs-Davison asked Secretary of State for Scotland George Younger: "In view of renewed interest by certain politicians in the Irish Republic, will my right hon. Friend affirm, on behalf of Her Majesty’s Government, that though it be uninhabited, and notwithstanding any negotiations on the law of the sea, Rockall is sovereign territory of the United Kingdom and will so remain?"