London — As the British armada braces itself for a battle in the icy Falkland waters, Margaret Thatcher is faced with the perhaps equally difficult task of keeping public support of her tough stand from flagging.
Until now the British Prime Minister has managed to rally her political critics to the opinion that Argentina's military junta will only retreat from the Falkland Islands at gunpoint. The British public so far has given her overwhelming backing. And the West European allies have also rallied to her side.
However, with the possibility of a long and bloody clash between Argentina and the British fleet nearing by the hour, many analysts here expect political and public opinion to begin to shift.
Already Mrs. Thatcher has been taking fire from all three opposition parties - Labour, the Liberals, and the Social Democrats. She is charged with not searching hard enough for a diplomatic exit from the Falklands crisis.
Such criticism came to a head at a stormy emergency debate in the House of Commons April 29, broadcast nationwide. Labour Party leader Michael Foot assailed the Conservative government for not calling United Nations mediators into the dispute. Mr. Foot urged Mrs. Thatcher to dispatch Foreign Secretary Francis Pym to New York for talks with UN Secretary-General Javier Perez de Cuellar.
Mrs. Thatcher replied, ''If anyone can solve the crisis, it's General (and Secretary of State Alexander) Haig. The United Nations cannot always enforce its judgment.''
Although Mrs. Thatcher in her opening address to Parliament was unwilling to discuss the details of the American peace plan, she declared that it ''inevitably bears the hallmarks of a compromise.''
She added, ''The crisis was started by Argentina invading the Falklands and it can only be settled by an immediate withdrawal of Argentine troops.''
But Mrs. Thatcher stressed that the government was still open to last-minute negotiations. Earlier, after a Cabinet meeting at No. 10 Downing Street, Defense Secretary John Nott declared that Britain has not ''abandoned hope'' of a diplomatic solution to the Falklands crisis.
Most observers here, however, considered that a major clash between Britain and Argentina was imminent--probably within the next 24 hours. At 7 a.m. (Eastern daylight time) April 30 the British task force was scheduled to start enforcing a total air and sea blockade around the disputed islands, and Argentina's military rulers have threatened to strike Britain first.
The peace proposals sent to Buenos Aires and London by the State Department April 27 are viewed by Mrs. Thatcher's government as seriously flawed. According to the Foreign Office, there are four points Britain cannot accept:
* A withdrawal of the British fleet parallel to an evacuation of Argentine troops from the Falklands. (The British insist that, as a precondition for anything else, the Argentines must reverse their original invasion and pull out.)
* Any discussion of British sovereignty over the territory.
* The question of joint Anglo-Argentine administration in Port Stanley, the Falklands' capital.
* The US plan's failure to consider the wishes of the islands' 1,800 inhabitants in the dispute. (Other reports suggest that the wishes of the Falklanders will be considered under the US plan, but those wishes would not be binding.)
Public opinion for Mrs. Thatcher has been running high since the Falklands flare-up. Polls taken by the Economist magazine give her basic strategy more than 80 percent support; and, according to a recent Sunday Times poll, the proportion of Britons now backing the Conservative government and Mrs. Thatcher herself has jumped 10 percent over a sampling taken before the crisis.
But the polls also suggest that if British vessels are sunk and lives lost, the prime minister's position would be weakened. Reverses in the South Atlantic could presumably be paralleled by similar political reverses at home.
Before Argentina's ruling military triumvirate ordered the Falklands invasion three weeks ago, those few Britons who thought of Argentina at all considered it to be a distant land known mainly for its corned beef and amazing footballers.
Two of Argentina's World Cup players, Ozzie Ardiles and Ricky Villa, joined the London Club of Tottenham Hotspur and their dazzling footwork became the stuff of popular legend. But Ardiles returned home soon after the Falklands crisis. And Villa is often booed by rival clubs when he appears on the field.
''I wish Argentina hadn't started all this,'' said John Scanlon, north London butcher and ardent Tottenham fan. ''It would be better if they let the lads play football in peace. But someone has to show those dictators that you can't redraw the map of the world by force. Britain is right to defend the Falklanders.''
But a client in his butcher shop disagreed.
''Britain's response and the possibility that hundreds, maybe thousands, will die on both sides is all out of proportion,'' declared a thin scholarly man. ''There's nothing on the island but penguins and a few hundred sheepherders. Let's use the money spent on the fleet to repatriate the Falkland residents.''
This conversation and dozens of similar ones overheard here reflect the factthat although most British people are willing to back Mrs. Thatcher's showdown in the South Atlantic, they are not without certain misgivings.