London — Britain's proclaimed readiness to go to war with Argentina to regain sovereignty over the Falkland Islands is part of a two-pronged military and diplomatic strategy to solve the biggest foreign-policy challenge to the Thatcher government so far.
London hopes that Argentina will be persuaded to withdraw its occupying force from the tiny island group in the South Atlantic once it sees the size and power of the task force now being assembled and dispatched.
The task force is the biggest in the world outside of the United States and the Soviet Union, and represents almost two-thirds of Britain's fighting fleet. It numbers about 40 ships.
Latest statements here appear designed to keep up maximum pressure on the Argentine junta in Buenos Aires while the fleet steams to a rendezvous point at Ascension Island about 3,500 miles from the Falklands. The fleet is expected to be there in about two weeks.
A new element in British strategy emerged April 4 when Defense Secretary John Nott announced on television that Britain was fully prepared to begin sinking Argentine Navy ships in an effort to turn public opinion in Argentina against its military rulers.
Echoing the words of Prime Minister Margaret Thatcher in the House of Commons the day before -- the first weekend Commons session since the Suez invasion of 1956 -- Mr. Nott said, ''We are going to restore British administration to the Falkland Islands . . . even if we have to fight.''
Pressed about military and naval tactics, Mr. Nott suggested that public opinion in Argentina may change ''once they find they are losing their navy . . . once they see the impact of military action against their assets.''
The word ''assets'' seemed to refer to Argentine naval ships, though later in the same interview Mr. Nott refused to rule out any military option, including possible blockades or attacks on the Argentina mainland.
Meanwhile Britain continues to enlist as much diplomatic support as it can, from the United States, Western Europe, and Commonwealth countries such as Australia and New Zealand.
Mr. Nott, however, said April 3 that these efforts would ''probably'' fail, and on April 4 he said that success ''doesn't look very likely.''
Observers here consider that few Latin American countries will take Britain's side and that the General Assembly of the United Nations in New York will fail to support the 10-to-1 vote in the Security Council April 3 calling for immediate Argentine withdrawal.
The Soviet Union, although it abstained in the Security Council rather than casting a veto, is a heavy purchaser of grain from Argentina and is expected to support her diplomatically.
Whether or not British ships actually open fire, the prospect at this writing is that London, the closest US ally in NATO, is prepared to go to war with a Latin American country that President Reagan has been eyeing for support against leftist guerrillas in Central America.
It is such a sudden and disturbing prospect that Britain, as well as Argentina, will now feel pressure from the US and other countries to refrain from force.
President Reagan tried to persuade Argentine leader Leopoldo Fortunato Galtieri to halt the invasion, but Washington has taken no sides on the basic issue of sovereignty.
The speed with which the crisis has developed here has bewildered and surprised British public opinion.
What began as a comic-opera landing of a salvage crew on the Falkland dependency of South Georgia has mushroomed into the biggest test so far of Mrs. Thatcher's credibility as the ''iron lady'' of British politics.
The House of Commons April 3 erupted with bellicose criticism from her own back benches and from opposition Labour, Liberal, and Social Democratic parties that she should have sent naval ships a month ago to support British diplomacy when London newspapers began to carry reports of a tough Argentine line in negotiations over the islands.
Those talks have dragged on for many years. Buenos Aires has threatened force before and Mrs. Thatcher claims she had no way of knowing Argentina was not bluffing again. But the British dilemma is a cruel one. Warlike opinion may change as the prospects of a shooting war draw nearer.
While the Times of London called openly for the use of force on April 3, the Sunday Times April 4 was already sounding more cautious.
And the Sunday Observer was calling for a compromise that would recognize Argentine sovereignty but grant the islanders special status to preserve their democratic ways and ties with London.
This compromise idea has been put forward various times in the past but neither side has been able to accept it. Its proponents argue that it would recognize the reality of a British population 8,000 miles from London but only 400 miles from Argentina.
Any British invasion of the Falklands or a blockade would risk casualties and losses. There is as yet no way of knowing how the British public would react to a string of sensational newspaper, television, and radio stories about a war to protect 1,800 sheep-rearing islanders in an area so remote that most people have to pull out their atlases to find it.
To back up Mr. Nott's words, the British task force is clearly prepared for an invasion.
The new aircraft carrier Invincible is carrying Harrier jumpjet aircraft. Two amphibious warfare ships, the Fearless and the Intrepid, and other craft are carrying Royal Marines, Sea King assault helicopters (one of which is piloted by the Queen's second son, Prince Andrew), and other attack weapons.
Any invasion would risk killing islanders themselves. Argentina is expected to pack the island with troops during the next two weeks, holding the 1,800 islanders as hostages.
Another option hinted at by Mr. Nott is to use the nuclear hunter-killer submarine Superb, already in the South Atlantic, to sink Argentine ships until occupying troops withdraw.
Or the British could set up a blockade around the Falklands, or even of key Argentina ports on the mainland. It could declare that any Argentina ships seen in the blockade zone would run the risk of being sunk. This would mean being willing to shoot down Argentine aircraft, and would subject the islanders to hardship as well.
One problem for the task force is logistics over long distances. Argentina's Navy is much smaller, but would be much closer to home.
Behind British strategy is a moral obligation to the islanders, who, like the majority Protestants in Northern Ireland, make it clear they want to stay British. Britain seized the islands from Argentina by force in 1832.
The Thatcher government's credibility is on the line. If the task force strategy fails, the prime minister will face calls for her foreign minister, Lord Carrington, and Mr. Nott to resign.
The Falklands are Britain's communications base for its Antarctic territory farther south, whose mile-thick ice could be rich in minerals and even oil. Both Argentina and Chile may claim parts of Britain's territory when the Antarctic Treaty expires in 1991.
Then there is oil. Argentina is drilling off its own coast.
In 1971 the Argentine Army chief of staff, Gen. Rafael Herrera, revealed the contents of a report which he said had been drawn up by the Shell Oil Company and which he claimed showed enough oil between the Falkland Islands and the mainland to justify calling the area a ''new Kuwait.'' Shell later warned that the report was only preliminary and not supported by geologists. But if Argentina thinks oil is there, it will be even less inclined to withdraw.
If Argentina keeps the Falklands it would claim all seabed minerals, fisheries, and all future finds 200 miles offshore -- an area bigger than Italy.