Prime Minister Margaret Thatcher lost her second Cabinet member in two weeks today, as Trade and Industry Secretary Leon Brittan resigned under intense pressure from inside Thatcher's Conservative Party.

Brittan's resignation, which Thatcher tried adamantly to resist, was the latest chapter in the protracted Westland affair that has provoked the most serious crisis to confront her government in 6 1/2 years in office.

It followed Thatcher's acknowledgment in the House of Commons yesterday that Brittan had authorized and arranged for the Jan. 6 leak of an internal government letter that served to discredit then-defense secretary Michael Heseltine. Heseltine resigned Jan. 9, charging that Thatcher and Brittan were working to undercut him.

Thatcher also acknowledged yesterday that her office had approved the leak. While she said that she had not been consulted and thought that the letter should have been distributed in another way, she said she agreed that government duty required that the contents of the letter be revealed.

Politicians and commentators were divided tonight over whether Brittan's departure would quell growing criticism over the way the government has handled the month-long controversy. With near-daily revelations of questionable political activity and evidence of serious enmities within the Cabinet, it has gone to the heart of Thatcher's reputation for integrity and strong leadership and has sent her popularity plummeting in opinion polls.

Throughout the crisis, which began as an internal Cabinet debate over the rescue of the bankrupt Westland helicopter company, Brittan has been Thatcher's closest ally. He has absorbed much of the growing criticism hurled at the government from both the opposition and a growing number of Conservatives.

Many Conservative members of Parliament said they hoped Brittan's departure would stop the controversy from escalating. One commentator, Sunday Telegraph associate editor Peregrine Worsthorne, reflected the view of some that Thatcher's problem has not been one of perceived authoritarianism, but rather of perceived weakness.

"This is an example of a prime minister trying to practice non-bossiness," he said tonight. "It's been a disaster. She should have bossed Michael Heseltine out of the Cabinet much earlier. She should have had no nonsense about allowing Mr. Brittan to do her job for her instead of doing it herself."

"It doesn't matter a damn if she's lost two Cabinet ministers," Worsthorne said, "so long as she can jolly well show that she is boss in the future, . . . she'll recover the confidence of the British people in no time."

But opposition leaders clearly saw the Brittan resignation as removing the principal obstacle to a direct attack on Thatcher herself.

Labor Party leader Neil Kinnock said Brittan was merely "a casualty of this whole dirty business . . . . The prime minister," he said, "has still got a great deal of answering to do." Sensing blood, Labor politicians began making references to a "cover-up" and a "British Watergate."

Liberal leader David Steel and David Owen of the Social Democrats said Brittan was being made a scapegoat for difficulties for which Thatcher still was responsible.

"As each hour and day goes by, the web of involvement of possibly quite innocent officials seems to be getting greater and greater," Owen said.

Parliament is to hold an emergency debate Monday on the Westland affair. Thatcher canceled a planned country weekend to work on a statement for the debate.

While the question of the leaked letter first surfaced nearly three weeks ago, until yesterday it had been submerged under other elements of the Westland drama. The controversy began as a fight within the Thatcher Cabinet over which of two rival offers to bail out Westland should be supported.

Heseltine argued that a consortium bid by five European companies should be promoted by the government to conform with its policy of encouraging European defense collaboration. Thatcher and Brittan argued that the company itself should be allowed to decide, and the company clearly preferred an offer by the U.S. company Sikorsky Aircraft.

Heseltine said Thatcher was covertly maneuvering on behalf of Sikorsky out of misplaced pro-Americanism and irrational insistence on governmental noninterference in commercial transactions. On Jan. 3, a Friday, Heseltine wrote to the European group, affirming that a Sikorsky investment in Westland would effectively ruin Westland's chances of participating in other joint European projects.

This letter, which was made public, bolstered Heseltine's case and came on the eve of a decision by the Westland board about the viability of the two offers. Hours before the meeting was to take place, however, the government's chief law officer wrote privately to Heseltine saying there were some unstated "material inaccuracies" in his letter that should be corrected.

Selected portions of that second confidential letter were leaked to the Press Association, Britain's domestic news service. The Westland board voted to recommend the Sikorsky bid to stockholders.

The question of who had leaked the confidential document quickly came up in Parliament, and Thatcher, whose government has hunted government leakers mercilessly in the past, said she would organize an internal investigation. Yesterday, she revealed the results of the investigation.

The leak, she said, had come from Brittan's office, with his approval. Moreover, Brittan had called her office, and her aides had agreed to the leaking. Amid hoots of derision from Labor benches and dark faces on her own side of the aisle, Thatcher repeatedly was asked why the inquiry took more than two weeks when Brittan obviously knew who was responsible, and Thatcher herself could not have avoided knowing.

Sensing that the situation was fast getting out of hand, Conservative Party leaders last night assembled and concluded that Brittan had to go.