If taxes here could only be as admirably low as in the United States, Prime Minister Margaret Thatcher told a television interviewer last week, Britain might share America's low unemployment and higher standard of living.

The advantages of doing things the American way are a recurring theme for Thatcher. If only the British had more American-style initiative and get-up-and-go vitality, and less willingness to let big government do things for them, she often scolds her countrymen, prospects here would be brighter.

Such talk has always gone down poorly in opposition political circles. Lately, it also has begun to worry members of Thatcher's own Conservative Party and even some of its boosters in the U.S. government, who fear that pro-Americanism is becoming an electoral liability in Britain.

In a country that has always seen itself as providing mature counsel and example to its impetuous former colony, "Mrs. Thatcher has committed the cardinal sin of saying 'Why can't we be more like them?'," explained a western diplomat who did not want to be named.

Not only does Thatcher frequently hold up the American character for British emulation, but she also repeatedly has supported, or failed to criticize, U.S. policies that are widely unpopular in Britain as well as in most of Western Europe. So far this year, several of the crises Thatcher's government has faced have involved the United States in some way -- with Thatcher sometimes taking abuse for being on Washington's side.

Concerned Conservatives and interested observers see Thatcher as out of step with a population increasingly alienated from the United States and weary of a "special relationship" that lately seems to have involved more give than take. British opinion polls indicate a massive lack of confidence in America's ability to manage its superpower status to the satisfaction and benefit of Western Europe.

Columnists note that "Anglo-American relations have rarely been worse," and generally conservative newspapers like the Daily Telegraph have editorialized about Washington's "apparent obliviousness" to European opinion. Relations with the United States tend to play an ever larger part in both public and political debate.

With elections here less than two years away, the question of Thatcher's popularity is of more than academic interest to Washington. The opposition Labor Party, currently leading in the polls by as much as 8 percentage points, has vowed that it will send home all U.S. nuclear weapons in Britain and close down American military bases.

American diplomats here divide their time between trying to massage a more reasonable stance out of Labor and managing the bilateral relationship with Thatcher. They say they are acutely conscious that the United States is "going to be used" by all sides in the upcoming campaign.

"Sadly, we do not need opinion polls to tell us that there is a far stronger than normal mood of anti-Americanism in Britain today," David Owen, leader of the centrist Social Democratic Party and a former foreign secretary, told the American Chamber of Commerce Monday.

"On the personal level, it is a superficial reading," Owen said. "There is, however, a deeper mood of frustration with the United States that is more serious."

The proximate causes of frustration are obvious to any reader of daily newspapers or follower of parliamentary debates here. The U.S. military raid on Libya and the Reagan administration's apparent decision to end adherence to the SALT II arms control treaty are considered two of the more blatant examples of unwise U.S. policy made over European objections.

More controversy is predicted early next month, when the United States and the European Community are expected to impose tit-for-tat higher customs duties on agricultural exports in an ongoing trade war.

British and U.S. officials interviewed over the past week, as well as academic and political observers of the "special relationship," see these incidents as the most recent examples of a much longer and deeper trend throughout Western Europe as it gropes toward a new balance in the overall Atlantic alliance.

Britain, said one analyst, is "a paradigm" of that trend. "There is a slightly higher degree of anti-Americanism here" than in the rest of Europe, he said, because its target "can be personified in Mrs. Thatcher."

In the four decades since World War II, analysts said, generational and ideological changes on both sides of the Atlantic have led to inevitable disagreement. While Europe has been withdrawing from global responsibility, the United States has seen itself as more committed to defending perceived western interests in areas geographically far removed from the NATO sphere -- such as Libya and Nicaragua -- and to a more aggressive attitude toward the Soviet Union.

Alliance crises over differences in opinion are "nothing new," noted Lawrence Freedman, professor of war studies at King's College in London. From the 1956 Suez invasion, through the Yom Kippur War and the neutron bomb dispute in the 1970s, to Libya and SALT II, they have been "corrosive rather than destructive," Freedman said.

Rather than allowing the alliance to crack, there is a growing feeling in Europe that "we ought to be thinking more coherently about how to manage" the crises "so that they don't damage the alliance," said a British official.

One answer has been a move toward more political unity among the alliance's European members. Over and above domestic political battles, Western Europe has become more of a regional entity, with a broad coincidence of interests and views on a number of issues. By channeling these agreements into unified positions, Europe can speak with a louder voice to balance that of the United States in transatlantic councils.

"It's absolutely pointless us spending our time whining" about U.S. policy, said David Owen in an interview. "We need to put our act together and come at you."

Through a united stand on trade with the United States, efforts to coordinate positions on East-West issues like arms control, and agreements on weapons production and purchases, some progress has been made. Prompted in part by Reagan's SALT II announcement and concern that the alliance was drifting apart on a range of foreign policy issues, European Community foreign ministers last week ordered a special study of ways to improve their dialogue with Washington.

Attempts to "Europeanize" their individual policies give at least the impression of balance with the United States and are popular with the European electorate. In most instances, Thatcher has supported them and in some cases Britain has even led them.

This year, on issues where Europe has differed with the United States such as Mideast policy, sanctions against Libya and arms control, Britain has been in the lead.

Yet what appears to be dominating opinion here is a perception of Thatcher as kowtowing to Washington, sometimes at the expense of Britain and Europe, and a reluctance personally to question any U.S. policy in public, even if her government is on record in opposition.

The year began with rivalry between U.S. and European companies over the purchase of Britain's Westland Helicopters Ltd. Although she proclaimed neutrality, Thatcher made it clear she was on the side of the Americans. The "Westland affair" quickly was followed by a similar dispute over the proposed sale of component companies of British Leyland, the government-owned motor vehicle concern. Once her intention to allow their purchase by General Motors and Ford became known, Thatcher was forced to back down under intense pressure.

In both instances, she was accused of bending to U.S. dominance, and her popularity ratings dropped. Then came the Libya raid, which Thatcher supported, but which the British public, the opposition and many within her own party opposed.

Despite her government's strong opposition to the Reagan administration's intended abandonment of the SALT II limits on offensive nuclear weapons, announced last month, Thatcher has found it difficult to take a personal stand in public. Questioned in Parliament in early June as to whether "she believes that the president should abandon SALT II," Thatcher repeatedly responded with criticism of alleged Soviet violations of the treaty, and a hope that "SALT II will continue to be observed on both sides."

"Why does she so regularly humiliate herself and this country by always dancing to President Reagan's tune?" deputy Labor leader Roy Hattersley asked the House of Commons.

Such rhetoric is relatively standard fare in British political debate. Besides, said a government official here, "foreign policy has not previously been in the forefront of electoral politics here."

The same official acknowledged, however, that "that may not be the case now." Combined with Thatcher's high praise for the American character and certain aspects of U.S. domestic policy, her relationship with the United States may turn into a significant vote loser.

Some in the Conservative leadership, while acknowledging current popular British antipathy toward the United States and its effects on Thatcher, believe Washington will move into the breach with pro-British policies to prove the "special relationship" still pays off. One example frequently cited is last week's Senate committee approval, after long debate and extensive British lobbying, of a newly revised extradition treaty between the two countries.

Additional proof, one official said, might come in U.S. concessions for some British exports during future trade negotiations with Europe.

But diplomats see that possibility as doubtful. "The Europeans are constantly aware of the United States," said one, and the United States "is not aware of Europe. That is to be lamented . . . but it's a fact, and it may be getting worse."

Thatcher, the diplomat said, "ought to be more cautious" about putting her eggs so visibly in the American basket.