It would not be possible for the UK to argue that it has a claim through prescription and the length of occupation because the original taking over the Argentine colony was not legitimate, as the islands were not res nullis.  In the Chamizal Case (Mexico vs United States), the ICJ rejected the right to title by prescription invoked by the United States because "the physical possession taken by citizens of the United States and the political control exercised by the local and Federal Governments, have been constantly challenged and questioned by the Republic of Mexico, through its accredited diplomatic agents." [1]  [1] The Chamizal Case (Mexico, United States), Reports of International Arbitral Awards, 15 June 1911, Vol.XI, pp.309-347