A government plan to sell Britain's last major nationally owned vehicle manufacturer to America's General Motors has turned into a political battle here with strong anti-American overtones.

The controversy comes on the heels of last winter's fight over the U.S. purchase of a share of this country's only helicopter designer and manufacturer. It has led to angry charges that there is no part of British industry that Prime Minister Margaret Thatcher will not put up for sale, particularly if the buyers are American.

Drawn unwillingly into what they see as a domestic debate over Thatcher's free-market economic policies, U.S. diplomats here have struggled for equilibrium between anger and concern. In a recent letter to The Sunday Times, U.S. Ambassador Charles H. Price II offered some "tempering perspective," pointing out that in a time of massive British unemployment, one out of every eight manufacturing jobs here is attributable to U.S. investment.

Price was responding to a Sunday Times poll in which a majority of respondents said they "resent the extent of American influence on British industry, the economy, defense policy and television." Similar majorities said they have little confidence in President Reagan's judgment and do not think he can be trusted to look after British interests.

Fears of being swallowed up by huge U.S. multinationals are a familiar theme in much of the world, and no less so in Britain. The current upsurge here began early last month, when word was leaked prematurely of General Motors' "secret" negotiations to buy a major portion of British Leyland (BL), the ailing, state-owned vehicle manufacturer.

With problems including aging and overstaffed production lines and poor management, BL had posted significant losses and been propped up by billions in government subsidies during the past decade.

Although numerous details remained to be worked out, General Motors basically offered to buy BL's money-losing truck division as long as the Land Rover division -- maker of prestigious four-wheel drive vehicles sold around the world -- was included.

A simultaneous leak revealed that Ford Motor Co. was negotiating to buy BL's Austin Rover car division. Both GM and Ford have been involved in Britain for decades, initially starting up their own operations here, then progressively absorbing or competing into oblivion most of the domestic vehicle industry.

The sale of British Leyland would leave Britain as the biggest economy in the world without its own auto industry.

BL's luxury car subsidiary, Jaguar, was sold into private hands in 1984.

After the December-January debate over the sale of Westland helicopters to the U.S. Sikorsky company -- a political battle that cost Thatcher two Cabinet members -- news last month of the BL negotiations came as a bombshell.

Despite Thatcher's professed neutrality about who bought into Westland, Conservative former Prime Minister Edward Heath charged, the government "wanted Westland to go to the Americans. And now they want British Leyland to go to America.

"I personally can't understand it for one moment," Heath argued. "Not for one moment. I cannot understand why a Conservative government above all should want to behave in this way . . . . The British just don't want their industries taken over completely by the United States."

Scenting blood, the opposition Labor Party's trade and industry spokesman, John Smith, asked the House of Commons, "Is there no part of British industry which is safe from the destructive purposes of this government? . . . Is there nothing not for sale?"

Former defense secretary Michael Heseltine, one of the two Cabinet casualties in the Westland affair, and now a persistent critic of government economic policy, also has used the BL bludgeon against Thatcher. In a speech today to the American Chamber of Commerce here, he noted that much of Britain's recent economic decline was self-induced, but he said the trend was slowly reversing.

"Britain has got to perform better," Heseltine said. "We are performing better. But we've got to have some products left to perform with. If, every time we run into industrial difficulties, we seek foreign buyers," he said, "then we are on a one-way, downward path . . . ."

Heseltine, and others, maintain that their reluctance is not anti-American, but pro-British. They argue that British economic health -- and increased integration with Europe rather than the United States -- ultimately will benefit America by providing a more stable partner for the Atlantic Alliance.

It is Thatcher, the critics have implied, who has raised the specter of anti-Americanism as a scare tactic.

There is no question that Thatcher and her supporters have sought to attach the label to opponents of the GM deal. "I fear some anti-Americanism has been aroused," she told Parliament last month, "and I fear deliberately, in the United Kingdom about the future of British Leyland."

Thatcher backer Norman Tebbitt, former industry secretary who now is Conservative Party chairman, ignored Conservative complaints about the deal and blamed the Labor, Social Democratic and Liberal parties, which also oppose it.

Their protests, he said in his own speech to the American Chamber of Commerce last month, indicated a willingness to "damage both our Anglo-American friendship and, indeed, the prospect for jobs in Britain by using dirty and cheap anti-Americanism in pursuit of dirty and cheap votes for dirty and cheap political parties."

Government responsibility, Industry Minister Peter Morrison said, is to make sure BL has "a good future, in an expanded market, with more resources being put into them . . . , based in this country." General Motors can provide all that and more.

At the same time, the government argues, with strong U.S. diplomatic backing, that American investors have been good partners for Britain. Ford, which set up shop here in 1911, employs 60,000 workers in its British plants. General Motors, here since 1925, estimates that it employs nearly 100,000 directly and indirectly here. GM has a $2 billion investment plan in the works.

American officials here discreetly have let it be known that British investment in the United States -- nearly $40 billion by the end of 1984 -- is larger than U.S. investment here, which has remained fairly constant in recent years at about $30 billion.

"A certain percentage of the population here is not used to the fact that Britain is no longer a number one international power," said one U.S. diplomat. Britain, the world's largest car exporter after World War II, is confronting the fact that even if it could produce goods fast enough, it cannot sell enough of them here and has trouble selling them abroad.

Critics of the BL sale note that "portfolio investments" account for much of the British money in the United States. But the Americans counter that their own investment here -- primarily in high technology and the automobile industry -- came from manufacturing start-ups providing jobs and income, rather than from buy-outs of existing businesses.

But the intensity of the pressure has forced the government to back down somewhat. Ford's negotiations over Austin Rover have been suspended indefinitely. Time was allowed early this month for other British enterprises to enter their own bids against General Motors to take over the trucks and Land Rover divisions.

There were indications this week that Thatcher was seeking to persuade General Motors to buy only the trucks division without Land Rover, or to limit its bid to a 49 percent holding of BL.

But there was little sign that General Motors was willing to buy under those terms.