British diplomats have accused Argentina of plotting an economic blockade of the Falklands amid fears that Buenos Aires is attempting to stop all flights from Chile reaching the islands.

The government of Cristina Fernández de Kirchner has publicly threatened to halt the weekly flight operated by a Chilean-owned airline between Punta Arenas and Port Stanley.

It is the islands' only air link with South America and their main connection with the outside world. British officials believe the service will disappear in an attempt by Argentina to make the Falklands too expensive for Britain to maintain.

"If the LAN Chile flight is cancelled it would be pretty difficult to resist the already credible thesis that there is an economic blockade of the civilian population of the Falklands," said a senior British diplomat in the region on Wednesday.

The move, which diplomats predicted would come soon, would further isolate the disputed island chain and ratchet up tension with London on the eve of the 30th anniversary of the war between Argentina and Britain.

British officials said that if LAN resisted, Argentina would simply ban the use of its airspace.

Fernández signalled the escalation in a speech to the UN last September, when she said Buenos Aires might block the flights, negotiated during a thaw in relations in 1999, if David Cameron's government refused to discuss sovereignty of the islands – which Argentina refers to as Las Malvinas. "We'll wait a little longer, but otherwise we'll be forced to review the standing provisional agreements," she said.

Cameron has continued to refuse to hold talks and recently angered the Argentinian government by accusing it of "colonialism" in its campaign to win back the islands. Argentina says Britain stole the territory, 300 miles off its south Atlantic coast, in 1833.

Argentinian commentators reported last week that Buenos Aires was squeezing LAN, a view which is shared by British officials. The cancellation of the route would leave the Falklands entirely dependent on the twice-weekly 8,000-mile military flight from London via Ascension Island, a volcanic island near the equator.

Barry Elsby, a member of the Falkland Islands' legislative assembly, said: "This has been rumbling for many months. It's a possibility we live with on a daily basis. It would be sad, especially for the Chileans who work and live here, because they would have to leave. And it would be a shame for a nation like Chile to be dictated to."

Instead of a 560-mile flight home to southern Chile, the islands' estimated 250 Chileans would have to travel via London.

Elsby said relatives of Argentina's 600 war dead would also suffer by losing cemetery visits. Once a month the LAN flights stop in Rio Gallegos, Argentina.

He played down the economic and political implications of the 3,000-strong population losing its main link to the outside world. "It would be an inconvenience but nothing that would harm the Falklands," he said.

Others have been less sanguine and warned of damage to tourism and exports.

The row puts LAN, which has one of the region's biggest fleets of aircraft, and Chile's conservative president, Sebastián Piñera, in an awkward position. Neither can be seen to bow to a neighbour's bullying, but there is commercial pressure for an accommodation.

The Falkland Islands flights are a profitable but tiny part of operations for LAN, which requires Argentinian co-operation for much of its international business. The airline, which Piñera part-owned before becoming president, has been unsuccessfully seeking permission from Argentina for a Buenos Aires to Miami flight.

Argentina has cancelled landing rights at Aeroparque, the capital's domestic airport, for LAN's flights from the Chilean capital, Santiago, and São Paulo, Brazil. It has transferred these to Ezeiza, the city's international airport, a major drawback for LAN because it is farther outside the city and deters potential passengers. Chilean commentators speculated this was done to gain leverage over the airline.

Fernández is understood to have raised the issue of Falklands flights with Piñera during a UN meeting in New York last September. She was expected to do so again earlier this month in Santiago, but the visit was pushed back because of her thyroid treatment.