The renewed demand by President Cristina Fernández de Kirchner for the Falklands to be handed back to Argentina elicited a defiant response from the UK and Falkland governments , with David Cameron vowing to do everything he could to protect the islanders' desire to remain British.

The prime minister rejected Fernández's call to restore the Falklands's "territorial integrity" by returning them to Argentina. The islanders are due to vote in a referendum in March that is expected to give overwhelming backing for the territory to remain British.

"The future of the Falkland Islands should be determined by the Falkland islanders themselves, the people who live there," said Cameron. "Whenever they have been asked their opinion they have said they want to retain their current status with the UK. They are holding a referendum this year and I hope the president of Argentina will listen to that referendum and recognise it is for the Falkland islanders to choose their future, and for as long as they choose to stay with the UK they have my 100% backing."

The Argentinian president made her latest intervention over the Falklands 180 years to the day after the islands were "forcibly stripped" from her country. In a caustic letter to Cameron, which was also published as an advert in the Guardian and the Independent on Thursday, she accused the British government of "colonialism".

The Foreign Office criticised the Argentinian government for ignoring the wishes of the islanders and rejecting any prospect of imminent negotiations, as demanded by Fernández. In a series of tweets, it said: "The people of the Falklands are British and have chosen to be so. They remain free to choose their own futures and have a right to self-determination as enshrined in the UN charter. There are three parties to this debate, not just two, as Argentina likes to pretend. There can be no negotiations on the sovereignty of the Falkland Islands unless and until such time as the islanders so wish."

The Foreign Office disputes Fernández's claim in the letter that "Argentines on the islands were expelled by the Royal Navy and the United Kingdom subsequently began a population implantation process similar to that applied to other territories under colonial rule". It says there was no civilian population on the island in 1833, with the Royal Navy expelling an Argentine military garrison that had arrived three months earlier.

There was an angry response from the Falklands, with many people taking to Twitter to hail the islands' relationship with Britain. The @falklands_utd account , which supports the right to self-determination, tweeted: "Through our right to self-determination we choose to maintain our relationship with Great Britain … Kirchner can write as many letters as she wishes. They carry less weight than the paper they were written on." There was also some criticism of UK papers for running the advert by the Argentinian government.

Barry Elsby, a member of the islands' legislative assembly, dismissed Fernández's claim that the Falklands was a UK colony. "We understand that the Argentine government has put out a letter that both calls our home a colony and claims that the United Kingdom is ignoring United Nations general assembly resolutions," he said. "We are not a colony. Our relationship with the United Kingdom is by choice. Unlike the government of Argentina, the United Kingdom respects the right of our people to determine our own affairs, a right that is enshrined in the UN charter and which is ignored by Argentina."

Thirty years after Britain and Argentina fought a 10-week battle over the Falklands, Fernández has embarked on a sustained diplomatic campaign to attempt to assert Argentina's sovereignty claim, which has seen her clash with Cameron over recent months. With her approval rating flagging ahead of mid-term legislative elections in October, the renewal of hostilities is likely to strengthen the perception of some critics that she is trying to draw attention away from domestic problems by attempting to unite Argentinians behind the "Malvinas" cause.

In the letter, Fernández notes that the islands are 8,700 miles away from London and says that not only Latin America but the "vast majority of peoples and governments around the world" embrace Argentina's claim and "reject colonialism".

In an indication of the passions the issue still arouses, #Malvinas was one of the top 10 worldwide trending topics on Twitter at one point on Thursday, although there was also a surge of support for British sovereignty under the Falklands hashtag.