Taking the military offensive for the first time in its confrontation with Argentina over the Falkland Islands, Britain announced it had recaptured the remote South Atlantic island of South Georgia today.

British troops landed by combat helicopter from a few warships offshore and retook the port of Grytviken after a brief battle with a small Argentine occupation force, British Defense Minister John Nott said here tonight. The assault was launched by a vanguard of the naval task force Britain dispatched to the South Atlantic 20 days ago.

"The Argentine forces offered only limited resistance to British forces," Nott said in a statement read to reporters outside 10 Downing Street with Prime Minister Margaret Thatcher at his side. "So far, no British casualties have been reported. We have no information on the Argentine casualty position."

But in Buenos Aires, the military government said there were still some pockets of resistance on the island. The Argentine government said early in the day that British warships and aircraft had attacked the garrison on the island with "intense shelling" and that its forces were resisting. Officials there also reported that two British helicopters attacked an Argentine submarine in the main port of the South Georgia islands, a dependency of the Falkland Islands 800 miles to the west.

The military clash, the first for British naval forces since the Suez hostilities in 1956, came 23 days after Argentine troops seized South Georgia and the Falklands, which have been the subject of disputes between the two countries for nearly 150 years.

The British landing also came as U.S. Secretary of State Alexander M. Haig Jr. was seeking to fashion a negotiated settlement to the crisis after spending the past 2 1/2 weeks shuttling among London, Buenos Aires and Washington. He presented new U.S. ideas to British Foreign Secretary Francis Pym in Washington Thursday and Friday and had been scheduled to meet this afternoon with Argentine Foreign Minister Nicanor Costa Mendez, who arrived in Washington today. However, the meeting was postponed at Argentina's request.

Britain's invading troops were aided by a dozen Marine commandos who sneaked onto the island from a submarine Thursday and reported there were fewer than 50 Argentine troops defending it, according to press reports. The prime minister's office refused to confirm or deny the report.

British combat helicopters began the attack at dawn by firing on Argentine positions in Grytviken and attacking and badly damaging a surfaced Argentine submarine entering the harbor, according to British sources. While "a number of warships" shelled Grytviken, the helicopters began landing British troops at 4 p.m. London time (11 a.m. EDT), Nott said, and the Argentine defenders surrendered two hours later.

"Just rejoice at that news and congratulate our forces and the Marines," Thatcher told reporters as she and Nott refused to answer shouted questions about his statement. "Rejoice, rejoice," she said as she turned to walk back into 10 Downing Street with Nott.

More than 100 Argentine marines--similarly landed by helicopters from warships--seized South Georgia in fierce fighting with 22 British Marine defenders April 3, a day after the main Argentine invasion force captured the Falklands. South Georgia, an icy, mountainous island discovered by British explorer Capt. James Cook, had been ruled by Britain as an administrative dependency of the Falklands.

Retaking South Georgia, lightly defended by Argentina and lying outside the range of mainland-based Argentine warplanes, had been expected as Britain's first military move. Besides being a relatively easy objective, it is seen here as a pressure tactic in negotiations for a diplomatic settlement of the Falklands crisis, as a morale-raising return of the Union Jack to a part of what Argentina seized three weeks ago, and as an establishment of a staging base for part of the British task force.

Although the island, as near to Antarctica as it is to South America, is cold, snowy and wind-blown during the South Atlantic winter, it has fresh water, sheltered fjord-like harbors for large ships and buildings from an old whaling station. The area can be used by troops carried by the British naval task force for rest and for training on dry land.

South Georgia has no airfield for longer-range British planes to challenge Argentina's apparent air superiority over the Falklands. But the nearly 20 Harrier vertical-takeoff jet warplanes now aboard the two aircraft carriers in the British task force can, like helicopters, land almost anywhere.

British officials said tonight that recapturing South Georgia is both an act of self-defense under the United Nations Charter and a pressure tactic in negotiations to secure an Argentine withdrawal from the Falklands without more fighting. They said Britain regarded Haig's peace mission as being "still in play," despite the attack on South Georgia.

"The U.S. government was well aware that we had not ruled out the use of force," a senior official here said. Officials added that the Reagan administration was kept informed of specific British military operations on South Georgia as they occurred and not in advance.

Thatcher's government is waiting, British sources said, for the reaction of the Argentine government to the U.S. negotiating ideas based on written British and Argentine proposals and Pym's talks with Haig. "Problem points" in the American draft were "identified" in a message sent from London to Washington late last night, a senior source said. While the American draft contained fewer such problems than the last Argentine proposals, he added, "I have been trying not to spread any optimism here."

The immediate reaction from Conservative Party politicians was favorable tonight. Labor Party leader Michael Foot said in a television interview, "I doubt very much whether it's right if we took the action first. I doubt very much whether it is wise for us to take such action at this moment when the Haig discussions are still going on."

About 1,000 people took part in a march to 10 Downing Street to protest the use of force, the first public demonstration against Thatcher's policy. Tony Benn, a leader of a left-wing faction of the Labor Party, said, "It looks more and more as if what is at stake is Mrs. Thatcher's reputation, not the Falkland Islands at all."

Thatcher's Cabinet, which last met on Thursday, was aware of where the British forces were and what they were planning to do before the attack on South Georgia, sources said. Overall strategy requires Cabinet approval, they said, while orders for specific operations come from military commanders reporting to Thatcher and her "war Cabinet" of senior ministers.

That group--Thatcher, Pym, Nott, Home Secretary William Whitelaw, military chief of staff Adm. Sir Terence Lewin and Paymaster General Cecil Parkinson, who also is chairman of Thatcher's Conservative Party--met for three hours last night to discuss what Pym brought back from his talks with Haig and to decide on what message to send to Washington.

As the attack on South Georgia began, they went to the Royal Navy's operational headquarters outside London to be briefed in detail, as Thatcher had been on Friday. They then joined Thatcher at her country home, later returning to London. Thatcher briefed Queen Elizabeth II.

The Defense Ministry said British helicopters fired on the U.S.-built, World War II-vintage Argentine submarine Sante Fe just outside Grytviken harbor. Nott said the submarine "was detected at first light and was engaged because it posed a threat to our men and to the British warships launching the landing" on South Georgia.

The Defense Ministry said tonight that the submarine, which normally carries a crew of more than 80, was severely damaged, leaking oil, listing to port and possibly aground after limping into the port. No information was available from British officials on the fate of its crew.

The timing of the attack may have taken the Argentines by surprise. The Buenos Aires government late last week said harsh weather ruled out an imminent attack.

The main elements of the task force, the aircraft carriers Hermes and Invincible, are believed to be in the vicinity of the Falkland Islands.