Next week's islanders are expected to vote overwhelming to remain an Overseas Territority of the UK, but will Argentina listen?
A cache of documents detailing behind-the-scenes meetings and operations during the Falklands War have been released under the 30-year rule.
It took Margaret Thatcher "three minutes" to decide that Britain would sink the Argentine warship the Belgrano during the Falklands War.
New documents revealing former Prime Minister Margaret Thatcher's unpublished testimony to the Franks Inquiry into the Falklands conflict is "like a film script", according to a Professor of Contemporary British History.
Professor Peter Hennessy, of Queen Mary University of London, described Thatcher's recollection of the conflict as "vivid".
Fears France could allow Argentina to acquire deadly Exocet missiles at the height of the Falklands War strained Margaret Thatcher's relationship with president Francois Mitterrand close to breaking point, according to official files made public today.
Publicly Thatcher always praised Mitterrand for his support during the conflict, but papers released by the National Archives under the 30 year rule reveal the intense suspicion and distrust of the French in London.
At one point, a furious Thatcher warned the president it could have "disastrous" consequences for the entire Nato alliance if a fresh consignment of the French-built Exocets was allowed to reach Argentina.
Britain woke up to the threat of the Exocet on May 4, when a pair of Argentinian air force Super Etendard fighters attacked the British Task Force heading towards the Falklands and unleashed two sea-skimming guided missiles.
This photograph showing British marines deployed in Grytviken, South Georgia near the Falkland Islands has been released by the National Archive under the 30-year-rule.
Other documents released reveal that the Americans wanted to inform the Argentinians that UK troops would be landing on South Georgia as part of its diplomatic peacekeeping mission.
The British ambassador to Washington, Sir Nicholas Henderson, succeeded in talking the Americans out of it.
A secret plot by Libyan dictator Colonel Muammar Gaddafi to supply arms to the Argentinian junta in the midst of the Falklands War was dramatically unmasked by British agents, according to newly published documents.
A British air attache discovered the Argentines were using the airport at Recife in Brazil as a staging post for shipping weapons from Libya.
The attache had a source at the airport who was able to board an Aerolineas Argentinas flight and saw for himself boxes apparently packed with missiles.
The British government decided to embarrass the Brazilians into halting the flights by leaking details through a third country, in order to protect the air attache's source.
Margaret Thatcher insisted on paying nearly £2,000 towards the search for her son after he went missing in the Sahara desert amid concerns of a public backlash over taxpayers' money being used, newly-released files reveal.
Mark Thatcher went missing for six days in January 1982 during rally, along with his French co-driver, Anne-Charlotte Verney, and their mechanic.
They were eventually found after a search by the Algerian military.
Records released for the first time to the National Archives show that Mrs Thatcher paid a total of £1,784.80 for the search operation to avoid any criticism over costs to British taxpayers.
The British government considered pulling England out of the 1982 World Cup as war broke out over the Falkland Islands, according to documents released by the National Archives under the 30-year rule.
In the aftermath of the Falklands conflict, sports governing bodies were urged to pull out of competitions with Argentinian teams because players might find it "difficult to meet Argentina on a sports field" if fighting was continuing.
But the documents show that cabinet ministers debated whether pulling out of the 1982 Football World Cup in Spain would send the right message.
In the end, England played and was knocked out in the second round.
US President Ronald Reagan issued a last-ditch appeal to Margaret Thatcher to abandon her campaign to retake the Falklands and to hand over the islands to international peacekeepers, according to official documents made public today.
Files released by the National Archives under the 30-year-rule show that Mr Reagan called the Prime Minister on 31 May 1982 as British troops were closing in on final victory.
"The best chance for peace was before complete Argentine humiliation," he told her, and urged her "to hand over the Queen's islands to a contact group".
Mrs Thatcher replied that she would not consider a ceasefire before the Argentinians withdrew from the Falklands.