A London company that is wholly owned by a British energy conglomerate with annual sales of $1 billion and interests in North Sea oil dominates the economy of the Falkland Islands.

The Falkland Islands Co., which was acquired in 1977 by the Coalite energy group, owns 42 percent of the land on the two main islands and a substantial number of the sheep. It also owns the only bank and charters the only vessel transporting wool to Britain.

Between 1970 and 1975, before its takeover by Coalite, 96 percent of the company's after-tax profits were distributed to stockholders in Britain or "channeled into portfolio investments in the United Kingdom," according to a report compiled for the British government by Lord Shackleton in 1976.

The territory for which the British and the Argentines have been fighting since early April has often been depicted in press reports or in statements by British officials as inhabited by a rugged breed of fiercely independent sheep farmers.

Actually, few of the islanders own their own farmland. Outside the holdings of the Falkland Islands Co., there are only 40 private sheep farms in the disputed territory. Some are huge--up to 120,000 acres--and many have been in the hands of the same families for generations. Five of the 40 are owned by absentee landlords in Great Britain.

Commenting in 1976 on the islands' economic structure, the Shackleton report cited a "continuing history of dependence of a great majority of Falkland Islanders" and added that "scarcely any of them have a stake in the place."

None of this suggests that concern over the narrow commercial interests of British investors or big landlords was the main reason for Britain's forceful response to Argentina's April 2 occupation of the islands.

The government of Prime Minister Margaret Thatcher has charged that the Argentine occupation violated United Nations and other international resolutions stressing the right of local self-determination.

The Argentina takeover, British spokesmen further point out, made no provision for the wishes of the 1,800 islanders, who repeatedly have said that they want to remain British.

"In spite of the weaknesses of the economy, people enjoyed a pretty good standard of living and lived a way of life that they wanted," said a former Falkland Islander now living in Britain.

Nevertheless, as the Falklands crisis moves from the arena of the battlefield to the negotiating table in the coming weeks and months, the interests of private British companies, investors and landowners appear certain to loom larger.

"It is legitimate to raise the question whether 50 percent of the economy of the Falkland Islands should be determined by a London-registered firm that is owned by a chemical and energy company," Lord Shackleton said in a telephone interview yesterday. "It can be asked whether the company should be owned inside the Falklands."

Lord Shackleton has met with Thatcher recently and it is assumed that he has been asked to update his 1976 report and to suggest possibilities for a settlement that would serve the interests of the islanders.

Last month, Argentina submitted a number of proposals to U.N. Secretary General Javier Perez de Cuellar that stopped short of full Argentine sovereignty over the islands. One proposal was for Argentina to purchase the Falkland Islands Co. from Britain, thus obtaining control over nearly half the land in the disputed territories.

In an interview yesterday, Coalite's chairman, industrialist C. Edwin Needham, described the company as "potentially a very useful asset." He said his willingness to sell would "depend on the price."

But he stressed that "whatever we do would have to be appropriate to the interests of the islanders" and the British government.

Needham said that two or three years ago he was approached "indirectly" by an Argentine business group about selling the company, but there were no concrete discussions.

Coalite acquired the Falkland Islands Co. in 1977 as part of a much larger deal involving Coalite's purchase of the company's owner at the time, Charrington Industrial Holdings.

Revenues from the Falkland Islands Co. amount to less than $40 million a year and make up less than 2 percent of Coalite's revenues, according to Needham. However, in describing the company as a potentially "useful asset," Needham acknowledged he was following the results of seismic studies of the offshore oil potential of the South Atlantic near the Falklands.

Coalite is best known in Britain as a producer of smokeless coal, manufactured under a high technology process involving low temperature carbonization. It also distributes fuels, makes chemical raw materials, has an interest in Sovereign Oil and Gas (which provides service to North Sea oil operations) and is in a North Sea oil drilling consortium with Mobil.

Until now, Needham said, investors have tended to shy away from the Falklands because of the uncertain political climate.

As a result, the islands' economy continues to revolve around wool production and the wool trade, much as it did in the early days of the Falkland Islands Co., which was set up as a royal charter company in 1851, 17 years after the British took control of the islands.

This has created moderate prosperity, but an economic structure portrayed in the 1976 Shackleton Report as rigid and fixed.

The report said that, throughout the 1960s, the Falkland Islands Co. was distributing on average 80 percent of after-tax profits to shareholders in Britain.

This percentage rose sharply in the early 1970s when the company was acquired by the small British investment company of Dundee, Perth and London.

"The general pattern is to keep investment in the Falklands as low as possible and to channel undistributed profits to the United Kingdom," said Lord Shackleton's report.

At the same time, the company's monopoly over land and commerce created tensions and, in the 1970s, pressure for change.

Until 1980, the private sheep ranches had only one market for their wool: the Falkland Islands Co. Since then, they have had the option of using another British-based company, J. G. Field, as their wool marketing agent.

Colin Smith, a former employe of the Falkland Islands Co. who set up the marketing competitor, credits the new agency with forcing up the price at which the Falkland Islands Co. offered to buy wool from independent farmers. Smith said that all but three of the 40 independent sheep raisers used his agency to market their wool last year.

The local governing council several years ago passed legislation aimed at opening up some sheep-raising areas for purchase by local residents. Under the Coalite management, the Falkland Islands Co., in an apparent effort to soften criticism of its 131-year-old lock on much of the territories' best farming land, divested itself of 170,000 acres and 17,000 sheep near the town of Green Patch.

The land was subdivided into six tracts and, according to Needham, sold to local residents at "giveaway prices."

Although Needham said he had no direct involvement with the Falkands until 1977, he acknowledged that "one can't help but get involved emotionally." He said that long before the Argentine occupation he had urged the British government not to withdraw the patrol ship HMS Endurance from the South Atlantic, but this was opposed by "civil servants in the Foreign Office."

Now, however, he feels thinks the British are united behind the liberation effort.

"In Britain we're daft enough to fight for principle," he said. The the islanders "drink the same beer as we do. . . . They're British people."