Britain suffered its first deaths of the escalating war over the Falkland Islands today when an Argentine air attack set the destroyer HMS Sheffield ablaze, forcing the crew to abandon ship, and a Harrier fighter was shot down during another British bombing raid on airfields in the Falklands.

The Sheffield, a heavily armed Type 42 destroyer that was one of Britain's most modern warships and which normally carried a crew of nearly 300, was hit by a missile believed to have been fired by an Argentine warplane inside the 200-mile blockade zone the British are enforcing around the Falklands.

"The ship caught fire, which spread out of control," British Defense Ministry spokesman Ian McDonald said tonight. "When there was no longer any hope of saving the ship, the ship's company abandoned the ship. All who abandoned her were picked up."

Repeating the Defense Ministry statement in Parliament later tonight, as Prime Minister Margaret Thatcher sat ashen-faced beside him, Defense Minister John Nott added that "12 men are missing." Later, in the midst of heated debate, he broke in dramatically after receiving a message on the floor and said the death toll "may be as high as 30."

Combined with yesterday's news of the sinking of the Argentine cruiser General Belgrano, the British losses announced tonight added to a growing unease among politicians here and in other European nations that the conflict in the South Atlantic is escalating out of control. There were signs that Britain's partners in the European Community might not continue to support the Thatcher government with economic sanctions that they had expected to take the place of a shooting war.

In Parliament here, divisions appeared to be quickly deepening between hawks who now want the military timetable speeded up and a full-scale invasion of the Falklands launched soon and doves who fear the government has given up on diplomacy. Increasing numbers among the ranks of opposition Labor Party Members of Parliament are calling for an immediate cease-fire and submission of the dispute to the United Nations.

Even the most bellicose conservatives appeared stunned. Before tonight, the news here had been only of British victories since the bloodless recapture of the island of South Georgia nine days ago: the sinking of two Argentine ships, crippling of a submarine, shooting down of at least three Argentine planes, and successful bombing of airstrips on the Falklands.

British sources said the operations room of the Sheffield was hit by one of two radar-guided Exocet air-to-ship missiles fired from as far as 20 miles away by an Argentine warplane, possibly a French-built Super Etendard fighter-bomber, flying from a base in Argentina. The other of the two missiles, which skim above the waterline after being dropped from a plane until they hit their target, is reported by British sources to have missed.

Nott said in Parliament tonight that British ships "accompanying" the Sheffield picked up survivors from the sea. He said "nearly all the ship's company and captain are accounted for."

Adhering to strict military censorship, the Defense Ministry did not reveal the location of the Sheffield when it was attacked. But it could have been acting as a radar picket between the Falklands and Argentina in the blockade zone to give early warning of any air attack to the rest of the British fleet.

Or it could have been escorting one of the two aircraft carriers in the British task force that would have moved to within 90 miles of East Falkland Island for today's British bombing raids on island's airfields, the second wave of such attacks in four days.

One of a number of the carrier-based Sea Harriers participating in those raids was shot down by Argentine antiaircraft fire. "The pilot has been killed," ministry spokesman McDonald said.

"All the other Sea Harriers returned safely."

As in similar British bombing raids on the Stanley and Goose Green airfields on the Falklands on Saturday, both a long-range Vulcan bomber flying from Ascension Island and Harrier vertical-takeoff jets from one of the two aircraft carriers in the task force bombed the Stanley field. McDonald said the attack by the Vulcan, which normally carries 21 bombs weighing 1,000 pounds each, was "successful" and the Vulcan returned safely to base.

Saturday's bombing left the Stanley runway "cratered and unusable by large transport aircraft from the Argentine mainland," Nott told Parliament in announcing the air raid, but not any casualties, earlier today. "A further sortie was made today to render the airstrip unusable for light supply, communications and ground attack aircraft operating within the Falkland Islands themselves."

The Harriers also apparently returned to the Goose Green airstrip near Darwin, 55 miles west of Stanley on an isthmus in the middle of East Falkland, which also had been bombed on Saturday. This is where the Argentine government, in a communique today, said its forces shot down two of three attacking Harriers. The Defense Ministry here refused to say where the single Harrier it admits to losing was shot down, but it acknowledged that there was more than one raid on the Falklands by Harriers today.

Thatcher made no comment tonight on the first reported British combat casualties of the conflict. Only one British seaman was previously reported injured, in addition to a helicopter crewmen who died in an accidental crash.

Argentine forces suffered casualties in their invasions of the Falklands on April 2 and of the island of South Georgia the next day. This past weekend, by British count, they lost at least three warplanes and their crews, a patrol boat and its crew, and the several hundred men still missing from the Argentine cruiser General Belgrano, sunk by a British torpedo Sunday.

Politicians here were divided tonight over the immediate impact on public opinion of the now-significant casualties on both sides. But, recalling a recent opinion poll in which three of five Britons said they could not accept the loss of a single British life, even the most bellicose Conservatives warned the government against a long, bloody war.

Saying he did not understand why two destroyers escorting the Belgrano were not also torpedoed on Sunday, Conservative Alan Clark complained, "We have been too surgical about this. The danger is in this delicate approach, always looking over our shoulders" at world opinion.

Answering criticism in Parliament earlier today about the attack on the Belgrano just outside the 200-mile blockade zone, Thatcher said, "Had we left it any later, it would have been too late, and then I might have had to come to the Commons with the news that some of our ships have been sunk.

"The worry I live with hourly," Thatcher said, less than three hours before she was informed of the Argentine attack on the Sheffield, "is that Argentine forces in attacks both naval and air will get through to our forces."

An aide to the prime minister said she was informed of the destruction of the destroyer at about 6 p.m. (1 p.m. EDT) while at her office in Parliament. She will have a meeting of her "inner Cabinet" of senior ministers handling the Falklands crisis Wednesday morning.

The aide said he did not expect today's events to change the government's policy of gradually escalating pressure on Argentina. "We've got to be deliberate," he said.

Foreign Secretary Francis Pym insisted in response to skeptical questions in Parliament that the Thatcher government was still seeking a diplomatic settlement to avoid further conflict, although it still insisted that Argentina withdraw from the Falklands and give up its demand for guaranteed satisfaction of its sovereignty claim before negotiations can begin.

Pym tonight sent to the United States what were described here as "constructive proposals" for ending the dispute following his talks with U.S. Secretary of State Alexander M. Haig Jr. during the weekend in Washington. Pym also received tonight what were described as "not very specific" proposals from U.N. Secretary General Javier Perez de Cuellar and will respond to them tomorrow, government officials said.

Defense Secretary Nott acknowledged under questioning earlier today in Parliament that the Belgrano was "30 to 35 miles" outside the 200-mile blockade zone when the British subarine Conqueror fired two torpedoes at it. But he said the cruiser and the two destroyers were "closing on elements of our task force, which were only hours away."

The cruiser had "substantial firepower provided by 15 six-inch guns with a range of 13 miles and Seacat antiaircraft missiles" and the destroyers "were equipped with Exocet antiship missiles," Nott said. "The threat to the task force was such that the task force commander could ignore it only at his peril."

Attacks by Argentine jet fighters and bombers on the task force on Saturday and the discovery the same day of an Argentine submarine "clearly in a position to torpedo our ships," Nott said, "left us no doubt of the dangers to our task force from hostile action."

Nott revealed for the first time that this Argentine submarine was attacked by the British task force. "It is not known if the submarine was hit," he said, without disclosing how it was attacked.

Pointing to Britain's warning on April 23 that it would use force whenever and wherever necessary to protect its fleet, Nott told Parliament that only the crusier was attacked "and not its escorting destroyers so that they would have been able to go to the assistance of the damaged cruiser. We do not know whether they did so but, in so doing, they would not have been engaged."

But Nott repeatedly refused to disclose the position of the task force when the Belgrano was torpedoed--according to the Argentine government, southwest of the Falklands. The main body of the task force has always been assumed here to be northeast of the islands, as far as possible from Argentina's mainland air bases.

After today's parliamentary debate about the Belgrano's sinking and before tonight"s announcement of British losses, more than 50 left-wing Labor members of Parliament signed a motion calling for "an immediate truce in the war before more lives are lost" and urging that "the government should fully commit itself to genuine peaceful negotiations" with the help of the United Nations.

Labor leader Michael Foot told Thatcher the sinking of the Argentine cruiser "raises very great questions" about the government's often-repeated commitment to secure an Argentine withdrawal from the Falklands with a minimum use of force.

Deputy Labor Party Leader Denis Healey warned Pym that "this is already causing great concern among our allies and friends around the world" and could cost Britain "a great deal of support." He noted expressions of concern today from several of Britain's partners in the European Community and the Irish government's announced intention to seek a new U.N. Security Council motion calling on both Britain and Argentina to cease hostilities.

Throughout tonight's extraordinary debate following the announcement of the attack on the Sheffield, Thatcher appeared pale and grim-faced. Anger flashed on her face when Labor's Ian Mikardo asked "if the prime minister asks us still to rejoice," a reference to what she said nine days ago when British troops recaptured South Georgia without loss of life on either side.

Before Nott could respond, he was diverted by other news and then rose to say, "I did say that initial indications are that 12 men are missing. I regret to say that the latest news is rather worse. The number of deaths may be as high as 30. We do not have sufficient information at this stage to give firm news to the House."

At that point Thatcher dropped her head and her shoulders went limp. Pym, sitting next to her, slumped.

Nott had taken the unusual step of making an immediate statement on the loss of the destroyer in the House, with nearly all of Thatcher's Cabinet minister returning to the chamber at about 11 p.m. to hear it.

Opposition Labor members had angrily broken into a debate on legislation concerning local government in Scotland. After Nott finished answering questions about his statement, Labor forced an unusual adjournment.