The Iron Lady is back. After being badly shaken less than four weeks ago by Argentina's invasion of the Falklands, an angry uprising against her government in Parliament and the resignation of her trusted and influential foreign secretary, Lord Carrington, Margaret Thatcher confidently has risked everything on an uncompromisingly aggressive response to the crisis.

In recent Cabinet meetings, appearances in Parliament and a lengthy national television interview earlier this week, Britain's prime minister has left little room for doubt about her unyielding determination to restore the Falklands to British rule as rapidly as possible by any necessary means.

The recapture of South Georgia Island so soon after the arrival of the vanguard of the British naval task force in the South Atlantic demonstrated how swiftly she is ready to use force. Since then, she has warned of her intention to move just as expeditiously against the Argentine occupation forces on the Falklands, despite evident concern in her Cabinet and Parliament about such rapid escalation.

"She's way out in front of everyone," said a well-informed member of her Conservative Party in Parliament, who said Thatcher appears to have shrugged off recent pleas of caution from some Cabinet members. "It looks like she doesn't intend to mess about."

In the extraordinarily emotional House of Commons debate April 3, the day after the "national humiliation" of the Argentine invasion of the Falklands, a visibly shaken Thatcher was reminded of her "iron lady" sobriquet by an old parliamentary adversary, renegade Conservative Enoch Powell. He said, "In the next week or two, this house and the nation, and the right honorable lady herself, will learn what metal she is made of."

That question appears to have been answered, to the delight of Conservative Party right-wingers who have formed Thatcher's power base and the chagrin of a number of politicians in all parties who oppose rapid military escalation of the crisis. Most of them have not voiced their misgivings publicly.

"There is not an ounce of bluff" in Thatcher's rigid stand and recent strong warnings, said one diplomatic source here. "She intends to strike [the Argentines] a mighty blow. She has been genuinely outraged."

Operational decisions during the crisis have been made by an inner cabinet including Thatcher, the new foreign secretary, Francis Pym, Defense Secretary John Nott and Paymaster General Cecil Parkinson, the chairman of Thatcher's Conservative Party.

Thatcher's full Cabinet has been kept informed on a less frequent basis of the inner cabinet's decisions and Thatcher's overall strategy. Some Cabinet ministers privately have questioned whether Thatcher has given the negotiating process enough time and emphasis in recent days, according to informed sources.

But Thatcher still has strong majority support in the Cabinet, these sources said, and appears to be pushing to the limit her authority as prime minister to exercise her own discretion.

"She has always led from the front," said one source close to Thatcher, who acknowledged that she reached her "low point" in the "shattering" experience of failing to dissuade Carrington from resigning just a day after Parliament resounded with shouted demands for her own resignation.

"She has been climbing back ever since then," the source said. "She has this remarkable capacity to put a reverse behind her. So many people underestimate her sheer physical, hard determination under pressure."

"I do stand very, very firmly for certain things," Thatcher said in this week's BBC television interview, "and I am here [as prime minister] because I do."

"I'm standing up for the right of self-determination" for the Falklands' 1,800 staunchly British inhabitants, she said. "I'm standing up for our territory. I'm standing up for our people. I'm standing up for international law."

Thatcher compared the Argentine invasion of the Falklands to an airplane hijacking. Without a tough policy, she said, hijackings increase. off again.' That's the way to stop hijacking.

"Similarly," she said, "to see that an invader does not succeed is to stop further invasions and to really stand up for international law against international anarchy."

The British people appear to agree. A poll conducted this week by the respected MORI opinion firm indicates Thatcher's Conservatives have pulled well out in front of the opposition Labor Party and the Social Democratic-Liberal alliance, with 2 out of 5 respondents saying they would vote for the Conservatives if an election were held today. Thatcher's personal approval rating, which had dipped badly due to Britain's prolonged economic woes, has reached 42 percent--up nine points since the crisis began. She indicated she was ready to do only three things to help Argentine President Leopoldo Galtieri "save face." She would pull back the British task force after Argentina had completely withdrawn its forces from the Falklands. She would allow a U.S. or international peace-keeping force to supervise the withdrawal while British officials resumed civil administration of the islands. And she suggested that the Argentine flag could fly over some form of diplomatic mission there.

Thatcher and her aides appear to be unruffled by this week's erosion of opposition Labor Party support for her strategy. Government sources dismissed Labor leader Michael Foot's demands that Thatcher forgo further use of force while seeking United Nations intervention as an attempt by Foot "to bail out of the consensus" under pressure from left-wing pacifists. They noted that other Labor members of Parliament continue to support a firm approach.