Parliament's police guards were among the first to realize how serious the situation was when they saw the chief of Britain's naval staff, Adm. Henry Leach, unmistakable in his uniform, arriving at the House of Commons for an 8 p.m. meeting with Prime Minister Margaret Thatcher in her private office.

They were joined by Defense Secretary John Nott, the deputy foreign secretary, Humphrey Atkins, and the top civil servants of their departments. Absent was the foreign secretary, Lord Carrington, who was in Israel on what had appeared that morning to be more pressing business--an error in judgment that would lead to his resignation five days later.

It was at this three-hour meeting on March 31 that Thatcher said she first expected Argentina to invade the British-ruled Falkland Islands. Her conclusion was based on intelligence reports from British and U.S. sources that until then had not been accepted as proof of an imminent invasion.

"They discussed some pretty crazy ideas about what should be done that night," said one source with knowledge of the meeting. But in the end, they realized that it was too late to threaten military action from 7,000 miles away or to send a British emissary to reason with the Argentine military government of President Leopoldo Galtieri.

Instead, they decided to ask the United Nations and the Reagan administration to try to prevent the attack, but the effort was to no avail. The invasion began just 36 hours after Thatcher's first crisis meeting ended.

It was only then that her government, reacting to the worst humiliation Britain has suffered since its ill-fated Suez adventure in 1956, reacted in a way that appears to have surprised Argentina as much as its invasion of the Falklands surprised Britain. With impressive speed, the British put together and dispatched its biggest naval task force since Suez, ready to fight the biggest naval battle since World War II.

Britain and Argentina have rushed to the brink of war, restrained now by Secretary of State Alexander M. Haig Jr.'s shuttle diplomacy, because of the same miscalculation in both capitals. After 150 years of sovereignty claims and 15 years of negotiations punctuated by harmless episodes of saber rattling, neither really believed the other would fight over the Falklands.

"This is crazy," said one worried member of Parliament as the Gilbert and Sullivan atmosphere of the first hours gave way to fears about military conflict that could cost Britain many lives and half its Navy, jeopardize economic recovery and topple Thatcher from power. "Here it is 1982, and we're going off to fight a colonial war in the South Atlantic, for God's sakes."

Critics of Nott blame him for encouraging Argentine military ambitions by selling British warships. The only Royal Navy vessel stationed in the Falklands as a symbol of the British commitment to their defense, the Antarctic survey ship Endurance, had been named as one of those to be sold or scrapped.

Critics of the Foreign Office blame its diplomats for indicating to the Argentines over the years a willingness to bargain away sovereignty over the Falklands, only to back down under pressure from representatives of the islands' 1,800 residents and the London lobby of economic interests there. British diplomats apparently failed to realize how impatient Galtieri's government had become about this after the last formal negotiating meeting at the United Nations Feb. 26 and 27.

Although the British thought they had won a compromise of Argentina's demand that the talks be accelerated, Galtieri sent diplomatic messages to London that this was not good enough. If negotiations were not speeded up, Argentina's Foreign Ministry warned on March 1, "Argentina maintains the right to put an end to this mechanism and freely elect the action that is most in its interests."

During the following days, the Argentine media and reports from British correspondents in Buenos Aires made clear that this was a threat to use force to settle Argentina's sovereignty claim. Carrington later acknowledged that there had been "bellicose noises in the Argentine press" as long ago as early March but that this was not unusual.

But on March 19, a group of Argentine scrap dealers landed on the island of South Georgia, a British-ruled dependency of the Falklands about 800 miles to the east. Before beginning contracted salvage work on an old whaling station, they refused to observe required immigration procedures and raised an Argentine flag.

When the Endurance was sent with a small party of British Marines to order the Argentines off, Argentina responded with several warships to prevent their forcible removal. Saying Britain had no right to order Argentines off Argentine soil, Galtieri's government threatened retaliation.

It was already too late for Britain to send a fleet to prevent an invasion, but it also was obvious that no one in London expected the Argentine move. A Thatcher aide later admitted trying "to laugh off" the South Georgia contretemps.

But by March 27 at the latest, and probably several days earlier, according to officials here, London received detailed "raw intelligence" of what its Buenos Aires embassy considered plans and preparations for an Argentine invasion of the Falklands.

At first, this evidence was judged ambiguous by the Foreign Office and the committee of senior civil servants that evaluates British intelligence. The sailing of the Argentine fleet on March 28, for example, confirmed by U.S. satellites, could have been for scheduled maneuvers with Uruguay.

"The evidence available to us shows that the Argentine regime took the decision to invade no earlier than March 20 and possibly as late as the 31st," a junior Foreign Office minister, Lord Belstead, said later. "Evidence before that time was to some extent contradictory and in our assessment pointed the other way. It is true, in the event, we were mistaken, but so were other countries."

Carrington first told Thatcher of the Argentine fleet movements on the morning of March 29 as the two British officials flew to Brussels for a Common Market summit meeting. Carrington returned to London March 30 to tell Parliament this was a "potentially dangerous" situation, but he referred only to South Georgia and not to any possiblilty of an invasion of the Falklands.

Carrington then decided to leave March 31 on a trip to Israel. British diplomats say a cancellation would have given the wrong message to Jerusalem, whose relations with London have been strained. But Carrington's critics say it gave the wrong message instead to Buenos Aires, which may have concluded that Carrington did not care enough about a military threat to the Falklands to concentrate on it.

Later that day, Argentina refused a request from London to receive a senior British emissary as soon as possible. This and more alarming intelligence reports prompted Thatcher to call the crisis meeting in her House of Commons office.

"The precise time we had information that it was an invasion fleet and it was on the way was Wednesday evening," March 31, Thatcher later told Parliament. "We took action then."

But all they could do was ask for help from the United Nations and President Reagan. When British Ambassador Nicholas Henderson went to see Haig the next morning, according to informed sources here, Haig appeared surprised at what he heard even though much of it came from U.S. intelligence sources.

Reagan's 50-minute telephone conversation with Galtieri and a U.N. Security Council call for restraint followed that night, but both failed to dissuade the Argentines. Although the invasion took place early the next morning, April 2, it took all day for the Thatcher government to be certain that the Falklands had been seized and to make their first reactive decisions.

But after that--although shaken by an emotional, acrimonious emergency debate in Parliament on April 3 and Carrington's resignation two days later--Thatcher's government quickly put together a U.N. Security Council resolution, economic sanctions against Argentina and the threat of considerable military force to come up with a strong hand to counter Argentina's occupation of the Falklands. With the bargaining positions now more equal, it is hoped here, Haig's shuttle diplomacy has a greater chance of success.