With debate raging over the future of Gibraltar when Britain leaves the European Union, Argentina feels it can also take advantage, claiming the islands off their coastline.
Spain are stating their right to Gibraltar and are trying to get the EU to take on their argument the rock is described as a colony rather than being British Overseas Territory.
Argentina is using this debate to also push its own rights to the Falkland Islands.
While Argentine president Mauricio Macri’s government is seeking an agreement with the UK over the island, opposition politicians feel they are not doing enough.
Defeat in the Falklands War in 1982 is an open wound in Argentina with large scale commemorations made each year for the dead.
Politician Daniel Filmus said: “Argentina will always have a debt for the fallen, the veterans and their families and we must honour their memory and the legislation they deserve.”
He continued: “We need to continue fighting for the ideal they fought and died for.”
At the same time nationalist groups have been coming to the Falklands and looking for trouble, claim Islanders.
There have been reports of them starting arguments, planting Argentine flags and writing inflammatory messages on social media.
Concern among Islanders has also been ratcheted up by the chance of left-wing politician Cristina Kirchner being re-elected as Argentine President later this year.
She is a fierce critic of British rule over the islands.
She said: “To speak of the Falkland Islands, of our rights, to defend our fighters cannot be separated from our overall politics. You cannot defend the Falklands and not defend national industry.”
While the British government said Brexit would have no impact on the status of the Falkland Islands, Argentina’s foreign minister Jorge Faurie has said Brexit would “enhance” their chances of taking control of the territory.
Mr Faurie and other politicians have compared the sovereignty of the Falklands with that of the Chagos Islands.
Earlier this year the UN’s International Court of Justice ruled the islands belonged to Mauritius and the UK should hand them back as their occupation was illegal.
