The Falkland Islands are to hold a referendum on their "political status" - hoping to bring an end to the continuing dispute with Argentina over the islands' sovereignty.
Their government's announcement comes as Falklanders prepare to mark the 30th anniversary of the liberation of the islands.
Three decades after Margaret Thatcher sent 27,000 troops and more than 100 ships to repel the Argentinian invaders, Buenos Aires continues to set its sights on claiming the territory it calls Las Malvinas.
But the Falkland Islands government said it hopes a referendum will send a firm message to Argentinian president Cristina Fernandez de Kirchner that islanders want to remain British.
Reacting to the announcement, Prime Minister David Cameron said that "the world should listen to the views of the Falkland Islanders and Britain will be "resolute" in supporting their choice.
In a statement he said: "Thirty years ago they made clear that they wanted to stay British.
"Now the Argentine Government wants to put that choice in doubt again, by shouting down the Islanders' ability to speak for themselves and punishing them for exercising their own free choice.
"That's why it's absolutely right that the Islanders have today set out how they intend to make their voices heard once more."
Foreign Office minister Jeremy Browne said that this was a "truly significant moment".
The Falkland Islands, a rocky archipelago in the South Atlantic, are 7,780 miles from the UK and 1,140 miles from Buenos Aires.
They have been under British control since 1833 - apart from the brief but bitter 74 days of occupation in 1982.
Gavin Short, chairman of the Legislative Assembly, said: "We are holding this referendum not because we have any doubts about who we are and what future we want, but to show the world just how certain we are about it.
"I have no doubt that the people of the Falklands wish for the islands to remain a self-governing overseas territory of the United Kingdom.
"We certainly have no desire to be ruled by the government in Buenos Aires, a fact that is immediately obvious to anyone who has visited the islands and heard our views."
"The Argentine government deploys misleading rhetoric that wrongly implies that we have no strong views or even that we are being held hostage by the UK military. This is simply absurd."
The Falkland Islands has a population of around 3,000 people, with just over half on the electoral roll and expected to take part in the vote.
The referendum will be organised by the Falkland Islands government and will take place in the first half of next year.
Mr Short said: "We have thought carefully about how to convey a strong message to the outside world that expresses the views of the Falklands people in a clear, democratic and incontestable way.
"So we have decided, with the full support of the British Government, to hold a referendum on the Falkland Islands to eliminate any possible doubt about our wishes."
The Falklands government said it intends to invite international observers to verify the outcome of the referendum.
It added that exact timings, the specific wording of the question and other details will be announced in the coming weeks.
Argentina's Ms de Kirchner has been heating up the debate over the islands as key milestones in the 1982 conflict have passed.
Last week she announced that Buenos Aires would be launching criminal proceedings against UK oil firms that are operating off the Falkland's coastline, saying they were operating illegally.
Britain has accused the country of implementing a number of economic blockades on the small, isolated islands and of acting in a "domineering way".
But British officials are adamant that there will be no change in the UK's sovereignty of the islands unless and until the Falklanders themselves wish it.
Foreign office minister Jeremy Browne, who arrived in the Falkland Islands yesterday, welcomed the announcement of a referendum.
"Only the Falkland Islands people can determine how they wish to be governed, so I very much support this initiative by the Falkland Islands government," he said.
"Indeed, I believe this referendum is a truly significant moment.
"It will give the Falkland Islands people the opportunity to send a clear message - not just to Argentina, but to the whole of the international community - that the islanders, and they alone, are masters of their fate."
He added that the British Government would respect whatever the outcome of the referendum might be.
"I call on all governments who prize democracy and human rights to do likewise," Mr Browne added.
"Whilst it is for the islanders to choose, let me be clear: the British government greatly values the links between the UK and the Falkland Islands.
"We believe these should continue and deepen, long into the future.
"And if this proves to be the will of the Falkland Islands people, then we in the UK will not just respect it, but will continue actively to defend this act of self-determination from those who seek to challenge it."
The government called for the referendum just two days before Ms de Kirchner is due to attend a UN committee in New York on de-colonisation.
During the meeting she is expected to put the Argentinian position on the Falkland Islands.
She will also be addressed by a group of young Falkland Islanders, most of whom were not born when the Falklands War took place in 1982.
Speaking from London yesterday, they said they often get drowned out by the arguments over sovereignty taking place between the UK and Argentina.
This will be the first referendum held on the islands, but in a poll in the mid-1980s, 94.5% of those who took part supported staying British.