Like her friend Ronald Reagan, Margaret Thatcher's personal popularity sometimes has exceeded public support for her policies.

Many Britons have been made uncomfortable by the sale of state-owned assets to finance government expenditure, the acceptance of high unemployment as a necessary price for economic readjustment and the emphasis on law enforcement and defense at the expense, as some see it, of social services.

But they knew that the nation was in decline, and bitter medicine has seemed to hold more promise of a cure than has any sweet syrup. Most have trusted that Thatcher knew what was best for them.

Likewise, her hectoring style and lecturing tone and a widespread reputation for bossiness and bustling, have been electoral assets rather than liabilities. It was with some affection that she was dubbed "the nanny of the nation."

But now it looks as if the nanny may have gone too far. Whatever the rights and wrongs of what has become known here as "the Westland saga," it has revealed an undercurrent of long-smoldering enmity inside the Thatcher government, which appears to be in disarray, and it has awakened hostility toward the prime minister among a significant portion of the population.

During the past two weeks, her personal approval rating has plummeted in the polls, and her Conservative Party has fallen into third place behind the two opposition groupings. According to one poll in the past several days, only 10 percent of the nation as a whole believes that she has told the truth about her government's policy and actions concerning Westland.

Not many people here understand the details of the Westland story -- which began as a competition between rival American and European companies to buy into Britain's bankrupt Westland Helicopters Ltd. Random comments suggest that most think it a peculiarly minor issue to have caused so much upheaval and so dominated political and public attention here during the past two weeks.

Even when defense secretary Michael Heseltine, who favored the Europeans, resigned on Jan. 9 over Westland, people listened more to what he had to say about Thatcher's style than to his thoughts about the issue itself.

He charged that Thatcher, while maintaining public neutrality over the bids, had taken behind-the-scenes action to promote the success of the American proposal. More interestingly, for most people here, he publicly accused Thatcher of "ill temper," authoritarianism and conspiring with her trade secretary, Leon Brittan, to have her way no matter what the cost.

Since then, a major political battle has ensued, with an unprecedented public hemorrhage of official and private documents and charges and countercharges. Brittan only narrowly avoided forced resignation as political outrage built to a crescendo last week.

With the controversy has come a new focus on the inner councils of Thatcher's government. The departure, by resignation or dismissal, of 17 members of her Cabinet since she took office in 1979 is seen by many as no mistake. Repeatedly, columnists quote the words of Lady Bracknell, from Wilde's "The Importance of Being Earnest" to the effect that while losing one Cabinet minister is unfortunate, the loss of two begins to look like carelessness.

What long has been the subject of opposition tracts -- that the Thatcher Cabinet has been filled with yes men as those with backbone have become fed up -- now is a subject for open discussion among Conservative backbenchers. Although his own popularity has not been overwhelming, Heseltine's charges that Thatcher repeatedly cut off debate within her Cabinet and connived to get her way appears to have struck a chord.

In political corridors, and among the public, those who long have seen her as a dictator have found new ammunition in Westland. Those who admired her style of leadership see her losing her grip as she is forced to defend herself against increasingly shrill attacks. "Her whole political reputation depends on being seen to be in control," said political scientist Alexander King.

Perhaps more lastingly, many seem to find the whole thing -- and by extension Thatcher -- tiresome.

Whether the Westland affair has any lasting effect on Thatcher remains to be seen. Loyalists in her government believe that it is of only passing importance, and will soon fade from the front pages. The next election is still a long way away, they say; she does not have to call it until 1988. And, despite her waning popularity, Thatcher still rates a comfortable margin above Labor Party leader Neil Kinnock, Liberal leader David Steel and David Owen of the Social Democrats in public perception as a person of prime ministerial caliber.

But one of the biggest dangers to Thatcher now is that it has become acceptable, even fashionable, among her erstwhile friends to criticize her and her policies.

Ever since coming to power, the Economist magazine editorialized this week, Thatcher "has made her personality a political issue. This personality -- energetic, self-willed, bossy -- has been the dominant force in British politics for a decade . . . . Her strong-mindedness and sense of conviction have been built into electoral assets, sometimes into national ones . . . .

"Mrs. Thatcher has held her party and governmental enemies at bay through her electoral appeal," the editorial concluded. "This appeal is waning . . . . Her style is no longer an asset. It is her biggest liability."