The British Broadcasting Corp., which built up a large stockpile of credibility with its World War II broadcasts to the oppressed peoples of Europe, boasts a rare distinction these days: it is jammed in Argentina and attacked by its own government in Britain.

Prime Minister Margaret Thatcher has registered "deep concern" about the publicly funded but autonomous network, which she says is not being sufficiently supportive of the war effort against Argentina. Foreign Minister Francis Pym said "an enormous number of people, millions, think that the coverage by BBC-TV isn't fairly done."

One of Thatcher's political opponents agrees--but for entirely different reasons. Radical leftist Tony Benn branded the BBC the "mouthpiece" of the government. Other opposition members have praised BBC coverage.

On the other side of the Falkland Islands war, Argentine Foreign Minister Nicanor Costa Mendez criticized the BBC for "giving false communiques."

The BBC is not the only member of the British press to be attacked. But the network, which was the symbol of the perseverance of British journalism in wartime, has come under the most public fire.

The BBC's problems at home began early when an announcer gave equal weight to British and Argentine reports of losses in the first fighting over the Falklands. A subsequent panel discussion on the talk show "Panorama" earlier this week was heavily weighted toward those who opposed military action in the islands. About 120 persons phoned to complain about the program.

The network, often regarded by conservatives as favoring the left, has also been criticized for allowing Argentine officials considerable time on programs. A cartoon in the Standard newspaper showed Thatcher dressed Argentine-style to deliver a speech on television while a producer explained: "Darling, it's the only way to get more exposure on BBC Television."

Pym suggested Monday that the public write to the BBC to complain about the coverage. As a result, the network has received more than 200 letters, two-thirds of them unfavorable, according to Alasdair Milne, director general-designate of the network.

Tonight about 100 members of Parliament from Thatcher's Conservative Party held a heated session with BBC Chairman George Howard in which several demanded that Howard either fire those responsible for the "Panorama" show or resign himself.

Nonetheless, the BBC is holding firm. Howard said he told the Conservatives that the BBC "has nothing to apologize for." Milne echoed that sentiment, saying, "The notion that we are traitors is outrageous. We at the BBC have reexamined our broad policy and will not change it. We have no sense of guilt or failure."

The Vietnam War brought home to Americans the impact of television on a war, but this is the first time Britain has gone through the experience. The BBC's problem, one of its journalists said, is that "the messenger is being blamed for bringing bad news." Ever since last week's attack on the destroyer Sheffield showed Britons that the Falklands fight would not be a walkover, there has been an upsurge of viewer complaints.

Some BBC employes say they suspect the criticism is linked to Britain's credibility problems over the information it is providing on the fighting. Responding to the charge that the network has given prominence to the Argentine version of events, they point out that the only film footage available on the fighting has come from Argentina.

A Ministry of Defense official, speaking privately, put the matter simply the other day. "We're losing the public relations war to Argentina," he conceded.

Hundreds of reporters are here to cover the war and the Ministry of Defense has been forced to hold daily press conferences. Even then, cameras are only allowed while the spokesman, Ian McDonald, reads his public statement. They must be turned off for his daily sparring with reporters seeking to eke out more information.

Last week McDonald spoke of Argentine "fabrications," contrasting them with the British "authoritative version." He added, "You can be sure our reports are true."

But that has not always been the case. McDonald's reports on the bombing of Falklands airstrips gave the impression that the raids had cut off all air links. But Argentina demonstrated otherwise with film showing planes landing on a bombed strip.

Britain's Sea Harrier jets took pictures of the destruction, but they have not been transmitted back from the Royal Navy task force yet. Nor has Britain been able to provide any film yet of the recapture of South Georgia Island 17 days ago.

The reason no footage has arrived from the task force is simple. The Royal Navy refused to allow satellite transmission equipment to be hooked up on the task force ships.

Until the prime minister's office intervened, the Navy was not going to allow correspondents to go on the task force ships to the South Atlantic, despite arguments that their reports would boost morale at home.