Thirty years ago the Falkland Islands was a windswept rocky outpost where shepherds tended vast estates for absentee landlords and the young went overseas in search of work, leaving behind a dwindling population and a severe shortage of women. Now the gales power wind turbines, the graduates are returning, the population has risen 65 per cent, and the Malvinas House hotel hums with oil contractors.

Stanley is still a sleepy town of one-storey whitewashed wooden houses with corrugated iron roofs painted red, green and blue, so clean and colourful it looks like a film set. But houses now sprawl more than a mile across the sea front as the economy has ballooned from £5m in 1980, to £109m in 2007, although the Falklands' entire GDP is still smaller than the budget of an inner-city London council. The islands are now economically self-sufficient, apart from the military, which costs 0.5 per cent of the UK defence budget.

But some things never change, such as the sniping words between British and Argentine leaders. As the 30th anniversary of the Falklands War approaches, a familiar spat about sovereignty of the islands has broken out. David Cameron has accused Argentina of "colonialism" and approved contingency plans to increase the British military presence on the islands. Argentina's Foreign Minister has responded angrily, describing the Prime Minister's comments as "insensitive" and Prince William's forthcoming tour of the Falklands as a provocation.

Behind the war of words there have been several years of mounting Argentinian economic pressure aimed at persuading Falkland Islanders to discuss sovereignty. But the economic squeeze may be counter-productive, hardening the attitude of young islanders who had been open to strengthening ties with South America.

Last month, the South American trading block Mercosur passed a resolution banning vessels flying Falklands flags from entering South American ports. On the treeless rocky landscape of the Falklands, it is hard to grow fruit and vegetables, and islanders are reliant on imports. Argentinian shipping-permit requirements imposed in 2010 have already ended a weekly shipment of fresh food and farming supplies from Chile, causing sharp price rises on the islands. Argentina also wants Chile to end the weekly airline flight from Puerto Arenas which would cut the Falklands off from the Americas altogether.

Speaking in the East Falkland accent that combines a New Zealand twang with a West Country burr, sheep farmer Paul Phillips said: "We used to get oat seed, and maybe turnip and swede, and the big advantage from getting it from Chile was the freight was cheaper. Now, bringing everything through UK, it don't take long for prices to go through the roof." Shula, his wife, adds that the price of a litre of milk has risen from 75p to £1.25 since the Chilean boat stopped. But high wool prices have shielded their farm from the impact.

Before 1982, the biggest landowner, the Falkland Islands Company, owned by Coalite, ran seven farms accounting for 43 per cent of the total acreage. After the war, the land was divided and sold to islanders. Most is now owned by smaller family farms.

Assembly member Mike Summers said: "It was feudal and colonialistic, but what you see now is a modern egalitarian society with opportunity for everyone."

Robert Rowlands, who rose from humble beginnings to become a director of a prominent local fuel business, remembers the days of the sheep-ocracy, when a small elite met in the colony club and "the rest of us owned nothing. It's beyond our wildest dreams how it's changed. Now we are the luckiest working-class people in the world."

Sixty per cent of the islands' revenues come from selling fishing licences, mainly to Spanish trawlers catching squid. The income from the fisheries, as well as grants totalling £46m from the UK government, has transformed the lives of the islanders. Where once British soldiers yomped across marshy scrubland, roads have been built, reducing the isolation of many farms.

More than two-thirds of the residents own four-wheel drives, islanders order deliveries from Tesco.com and Argos.com and the fashion-conscious choose their clothes from the Asos clothes website. The population has risen 65 per cent since 1980 to 3,000, with almost half the population under the age of 35. With a generosity which would make UK students green with envy, the Falkland Island government pays for all young islanders who get five good GCSEs, to live and study for A-levels and degrees in England. Most of those young graduates return to the ilands.

There also many foreign workers servicing the economy, with the search for oil fuelling the influx. Five small oil companies hold licences to explore the waters surrounding the islands, and British-owned Rockhopper Petroleum says it has found a site with 350 million barrels of petroleum. If tests prove positive, it hopes to start extractionin 2016, although not all independent analysts agree the site is economically viable.

It is hard to find anyone against oil drilling on the Falklands. Another assembly member, Jan Cheek, said: "There is more risk of a spill from a passing tanker than from a properly regulated oil industry."

Oil wealth also gives the Falklands the possibility of becoming independent, paying for its own defence, and perhaps even overseas aid for the UK or South America, says Mike Summers, but this is a "long, long way off".

Yet the prospect of an oil boom, coupled with a growing sense of unity and confidence among the left-wing governments of South America, has hardened attitudes in Argentina. During the 1990s, the Carlos Menem government signed deals on fishing and hydrocarbons in the Falklands, but now Buenos Aires has pulled out of all talks and says it will discuss nothing except sovereignty. The Foreign Office and Falkland Island government are willing to discuss anything except sovereignty.

This impasse has frustrated young graduates in the Falklands, many of whom would be happy to increase trade, tourism and environmental co-operation with Argentina, without discussing sovereignty.

Zoe Luxton, a vet, said: "There are some people who lived through the conflict who are so traumatised, I don't think they could ever think rationally about making links with Argentina. We could quite easily make trade and tourism links, but sovereignty is not an issue. No one wants to be Argentinian. End of."

Graduates speak of their willingness to talk to Argentinian professionals and even, in the future, to join Mercosur. But with Argentina refusing even to talk, said Mr Summers, such a gradual rapprochement is impossible.

"The common-sense position would be for Argentina to be nice to us, talk to us about all sorts of practical issues and get on with people here, then over time our children or our grandchildren or our great grandchildren may take the view that they would be better off associated with Argentina or Mercosur than the United Kingdom," he said.

"That would be a proper exercise in the right of self-determination, but colonising first or doing it by force is not."

Thirty years of conflict: Claim and counter-claim in an endless dispute

1982 2 April: Argentine troops invade;

13/14 June: Argentinians surrender.

1990 UK lifts trade embargo but Argentina maintains its claim.

2001 Ban lifted on Argentine private aircraft and vessels visiting.

2009 Argentina claims wide expanse of ocean, including Falklands, at UN.

2009 Britain rejects calls for talks over future sovereignty.

2009 Argentine parliament passes law that claims the Falklands.

2010 British firms drill for oil off the archipelago. Argentina responds by imposing controls on nearby ships.

2010 Hillary Clinton says US wants to see both countries resolve issues in a "peaceful, productive way".