Britain's undeclared naval war with Argentina over the Falkland Islands has led to open warfare on Fleet Street.

The two largest popular British newspapers have been in a full-scale slugging match for the last two days over patriotism in the war cause.

The Sun--which, under the ownership of Australian press magnate Rupert Murdoch, climbed from the doldrums to become Britain's largest circulation daily on the popularity of topless women pictured daily--yesterday charged its chief rival with treason. The Sun accused the Daily Mirror of trying to appease the Argentine government, apparently because of its open support for a cease-fire in the South Atlantic.

The Mirror struck back today with a full-page comment under a huge block-type headline describing The Sun as "The Harlot of Fleet St."

Behind the sensational press rivalry, however, there is serious concern here "that in war, truth shall not be the first casualty," in the words of British Broadcasting Corp. Chairman George Howard.

Even though Argentine claims of major military successes against the British have little credibility here, the Defense Ministry is open to charges of news management, and its press briefings are often less than enlightening. Citing the need for operational secrecy, ministry spokesman Ian McDonald refuses to answer many of the reporters' questions or gives answers that at times appear to be misleading about British military strength in the war zone.

The remark by BBC head Howard was in response to a statement in Parliament by Prime Minister Margaret Thatcher this week that "many people are very concerned indeed that the case for our British forces is not being put over fully and effectively" within the country.

Thatcher, who is known for paying little attention to the media, said she understood that "there are times when it seems that we and the Argentinians are being treated almost as equals and almost on a neutral basis.

"I understand that there are occasions when some commentators will say that the Argentinians did something and then the British did something," a reference to broadcasts of the BBC, Britain's publicly funded but autonomous radio and television service.

"I can only say," Thatcher added, "that if this is so it gives offense and causes great emotion among many people."

There was a sense of deja vu for Americans, recalling the Vietnam War when U.S. journalists cut their teeth on the idea of criticizing their government during war.

The BBC's Howard, in remarks that could have been right out of Vietnam a decade ago, compared "our ability to report contemporary hostilities and the ability we had to report past conflicts. We now do have the opportunity not only to work in the aggressor's country but the ability to report closely on his attitudes."

He stressed, however, that the BBC "is not, and could not be neutral as between our own country and an aggressor."

The BBC was among those charged with treason by The Sun for mildly questioning British combat communiques. The Manchester Guardian was pilloried for a cartoon questioning whether British sovereignty of the Falklands was worth the death toll.

But The Sun reserved its strongest criticism for the Mirror, its circulation rival, saying, "What is it but treason for the Mirror's appeasing the Argentine dictators because they do not believe the British people have the stomach for a fight?"

Never a paper to lack imagination, The Sun "sponsored" a missile on one of the planes in the British task force. Its reporter wrote "Up yours, Galtieri" on the side of a missile, a reference to Argentine President Leopoldo Galtieri.

The Sun also has run a series of jingoistic headlines over the last month. The most memorable one, atop a story about a partial British rejection of Argentine settlement ideas almost three weeks ago, read "Stick it up your junta." The headline has now been memorialized on T-shirts.

The Daily Mirror said in its riposte today that The Sun "has long been a tawdry newspaper. But since the Falklands crisis began, it has fallen from the gutter to the sewer."

The Defense Ministry's briefings have drawn criticism. At a recent session, spokesman McDonald refused to give answers or declined knowledge on a number of questions including the following: where was the Argentine cruiser General Belgrano when it was torpedoed and how close was it to the British naval task force? Who gave the command to torpedo the ship? Where is the Argentine fleet? Have Falkland Islanders suffered any casualties? Have British forces tried to carry out helicopter landings on the Falklands as Argentina claimed?

McDonald's answer to the last question was a masterpiece of obfuscation:

"What I have said throughout to that kind of very interesting question," he said, "is that interesting though it may be, I have throughout the whole of the last four weeks never made a comment on it but have always said that I hope no one will think my comment means more than quite simply no comment."