London — Unless United States or other mediation succeeds, the prospects for the government of Prime Minister Margaret Thatcher being able to extract itself successfully from the Falkland Islands venture do not look good.
With the most powerful naval fleet ever sent from Britain in peacetime steaming toward the Falklands, with the prime minister herself refusing to resign and declaring, ''Failure? The possibilities do not exist,'' and with new Foreign Secretary Francis Pym just taking hold, the government's room for maneuver seems small.
Mrs. Thatcher and her aides say the object is ''regaining'' the Falkland Islands - to fly the British flag once again over Port Stanley, now renamed Puerto Rivero.
They want to achieve it by diplomatic means but freely admit it is ''difficult'' to see how. They privately take heart in Argentina's apparent willingness to listen to US mediation.
Meanwhile, they are pinning everything on the power of their 36-ship task force with its nuclear missiles, amphibious landing forces, jump-jets, and attack helicopters to do two things: (1) back up British diplomacy at the negotiation table, and (2) worry Argentine public opinion to the point that, hopefully, the ruling generals will withdraw.
Aircraft and helicopters were deliberately put on deck as the carriers Invincible and Hermes left Portsmouth April 5 in an effort to convince Argentine television viewers that Britain means business.
The British hope is that leftist and trade union opposition to the Argentine junta's failing economic policies will be exacerbated.
The British Cabinet says there will be no direct talks with Argentina until invasion forces are removed from the Falklands.
Cool heads here are thankful that it will take between two and three weeks for the ships to reach the Falklands. That gives diplomats some time to find a nonshooting solution.
London asked the European Community in Brussels April 6 to help with diplomacy and economic sanctions against Argentina, which exported goods worth about $2.1 billion to the EC in 1980. The EC condemned the Argentine invasion and urged the Organization of American States in Washington to join in making peace.
In a quick show of support for Britain, West Germany, France, and Belgium agreed April 7 to block the sale of frigates, submarines, and other military items to Argentina.
It is being asked here what Mrs. Thatcher could accept short of complete Argentine capitulation. With Buenos Aires filling the Falklands with armed troops, such capitulation is seen as highly unlikely at the moment.
Among factors tying Mrs. Thatcher's hands are the extremely patriotic mood of the Conservative Party, a temptation to equate the Falklands takeover with the Nazi invasion of Poland at the start of World War II, a sensational and baying Fleet Street press, and opposition parties eager to undermine Mrs. Thatcher in private while supporting the task force in public.
A widespread view in the newspapers and in the House of Commons is that dictatorships must be resisted, and that Argentina ''must not be allowed to get away with it.''
Very few voices are being heard here suggesting that the size of the task force might add up to overkill, or that the Falklands in the South Atlantic cannot begin to be compared to Western Europe in strategic, diplomatic, or military importance.
But these voices could grow. They argue that of course Britain has a duty to protect the 1,800 islanders, but they add that Britain failed in that duty the moment Argentina invaded. It is now too late to attack without endangering the islanders themselves, the argument goes - so Britain's dismal, but necessary, job is to negotiate the best terms possible for the islanders, allowing them either to stay on with special status or to move to Britain or other countries to live.
This view holds that Britain simply cannot defend colonies 8,000 miles away any more. Better to retire gracefully than risk defeat and opprobrium by a warlike strategy.
The United States is unlikely to approve a British resort to force. When a British television reporter in the White House gave him a chance to do so April 5, President Reagan pointedly declined. ''We are friends of both sides,'' is all he said, and he later referred to the dispute as ''unnecessary.'' This was cold water to Mrs. Thatcher, who nonetheless has praised Mr. Reagan for his efforts to stop the invasion and for support in the UN Security Council.Mr. Reagan indicated, however, that the US was prepared to act as an honest broker or mediator.Pressure will build on London from other Latin American countries and from the third world to negotiate and compromise. The General Assembly, dominated by anticolonial third-world countries, is thought unlikely to support the Security Council call for an immediate Argentine withdrawal.Significantly, some leading members of the Labour Party's international committee, including member of Parliament Eric Heffer, made it clear April 6 that they did not want a shooting war.If her show of strength does not work, Mrs. Thatcher could reluctantly decide to settle for a diplomatic solution that grants Argentina sovereignty but tries to protect the islanders' democratic way of life.That cannot happen tomorrow: If it did, Mrs. Thatcher would almost certainly be forced from office, accused of a ''sellout.''Whether it can happen three weeks from now, when Argentina has had a chance to assess the British task force, and whether Mrs. Thatcher would resign if it did, is unknown.Islanders themselves want to remain British because 95 percent of their supplies come from Britain by ship and they send their wool to Britain for sale around the world.Argentina is a poor country, and the islanders fear they will be neglected if Argentina retains sovereignty and its initial enthusiasm for the takeover fades.One of the biggest tasks facing the new foreign secretary, Francis Pym, will be to judge at what point force might be counterproductive and whether to settle for a diplomatic agreement. He is a potential rival to Mrs. Thatcher for the leadership of the Conservative Party.The most disastrous result for Mrs. Thatcher would be to sink Argentine shipping, incurring the wrath of the third world, and find that she had only united Argentine public opinion instead of turning it against the junta.She would then have to decide whether to send marines ashore onto the Falklands, a move that could lead to islanders themselves being killed and would ensure that the nearly 17,000 British citizens and the additional 40,000 to 50,000 people with dual Argentine and British nationality living in Argentina would be interned.If she succeeded, she would be buoyed by a wave of euphoria, but Britain would have to hang on to the islands under constant siege by an angry and vengeful Argentina.If she failed, she would be under immense pressure to resign.This would remove from leadership in London a prime minister who is President Reagan's strongest supporter in Europe. It could lead to a rift between London and Washington, with the British disappointed at a lack of US support and Americans impatient at such drastic action over a remote set of islands.Criticism from Labour, Liberal, and Social Democratic parties aimed at the government's failure to anticipate the crisis is deeply worrying to Conservatives.For the moment, it increases the pressure on Mrs. Thatcher to stand firm as the task force proceeds.For two days she tried to persuade Lord Carrington not to resign as foreign secretary. But he said it was the only honorable thing to do in the face of what he called ''a humiliating affront to this country.''He remains widely respected for his integrity. He was in Brussels and Jerusalem just before the invasion, and he and his aides clearly misread Argentine intentions.Defense Secretary John Nott stays in office because he bore less responsibility for the diplomatic failure and because Mrs. Thatcher wants continuity of leadership for the task force.It is regarded as ironic in the extreme that the prime minister is facing her biggest test abroad rather than at home, where she has been unpopular over her monetarist economic policies.