London — Relieved at the successful recapture of South Georgia without loss of life, Britain turns with some apprehension to the far greater military and diplomatic challenge of the Falklands themselves.
The question here is ''What next?'' Prime Minister Margaret Thatcher's answer is: more military action soon, unless Argentina withdraws from the Falklands at once.
If its forces do leave, she indicates, negotiations will continue. It is taken for granted here now that Britain will cede sovereignty in return for assurances that the wishes of the 1,800 islanders will be respected.
The prime minister has jumped in hard to tighten pressure on Buenos Aires, warning the House of Commons time and again April 26 that ''time is running out.'' At one point she said that it ''may not be possible'' to force the Argentines to withdraw by negotiations.
The impression she gave, despite her protestations that talks were still taking place, was that she was tired of waiting. She could not, she said, keep the naval task force in ''wild and stormy weathers'' indefinitely.
This has led to predictions here that the next military step could be landing a small group of the Royal Marines' Special Boat Squadron (commandos) on a deserted area of East Falklands, one of the two main islands in the Falklands chain.
Despite an unconfirmed British government report that a full-scale invasion could come within two days of April 26, other strategists suggested that it was more likely that a reconnaissance group would be put ashore secretly. Private messages could then be sent to Buenos Aires warning of an attack to come if Argentina did not withdraw.
There must be time, many officials say, for Argentina to feel each escalating step of military pressure before the next is taken.
With military force now in play, Mrs. Thatcher and the British people move into a new phase of the crisis.
A steady 50 percent of those questioned in opinion polls so far have been opposed to the loss of British lives over the Falklands. Opposition Labour, Liberal, and Social Democratic parties are heightening pressure on the government to delay any new military actions until diplomacy has had more room to maneuver.
Labour leader Michael Foot said April 26 that ''if one initiative fails, another has to be started . . . What is legal is not necessarily also prudent. The search for peace must never be torpedoed by us.''
The Financial Times newspaper April 26 caught much of the apprehensive mood in an editorial that called for Britain to return to the UN Security Council to reaffirm its support before using force again. London, it said, should also offer to go to the International Court of Justice or accept UN trusteeship of the Falklands.
Britain, it went on, had already conceded that sovereignty was negotiable in previous talks:
''To reduce that approach to the absurd, Britain must recapture the Falklands in order to capitulate gracefully later . . . Argentina is wrong, but there is no need yet for a military showdown.''
The recapture of South Georgia turned out to be a straightforward affair. No British casualties had been reported at this writing, and only one Argentine was seriously wounded.
The Argentine commander on South Georgia surrendered on the morning of April 26, and according to Mrs. Thatcher, British forces took about 180 Argentine prisoners, ''including up to 50 military reinforcements'' who had been on the Argentine submarine Santa Fe.
(Mrs. Thatcher said April 26 that the prisoners would be returned to Argentina, Reuters reported.)
The British version is that the Santa Fe was fired on as it approached Grytviken harbor, because it posed a threat to British ships landing invasion forces.
Britain had previously warned Argentina that any naval craft, submarines, or aircraft approaching elements of the British task force would be liable to attack.
The British version of the fighting, very different from Argentine reports, is that it was all over in Grytviken within two hours, and that Argentine troops offered only limited resistance. By the morning of April 26 British troops had also taken the nearby settlement of Leith.
The British claim to South Georgia is clear. The island has never belonged to Argentina or Spain. Officially it is a British dependent territory administered from the Falklands only for convenience, and populated only by a handful of men from the British Antartic Survey.
The diplomatic and military situation on the Falklands is very different.
Argentina had only a small force on South Georgia but is reported to have reinforced the Falklands with 9,000 men since its takeover April 2.
The Argentine Air Force has been using the airport at Port Stanley, though reports that the strip has been strengthened to take Argentine Mirage fighters is discounted here.
Any British assault on the Falklands would bring Argentine Mirage and Skyhawk fighter bombers from the mainland. It would also meet heavy fire from the islands and would put at risk the lives of the Falkland Islanders themselves.
The case against an invasion, put by opposition politicians and the Financial Times, is that lives would be at risk to defend a way of life on the island that Britain cannot, in fact, defend in the longer term.