The roster of U.S. allies in Europe these days is distinguished by tottering governments. Domestic political problems, generally concerning economic policy, are battering administrations in West Germany, France, Spain, Italy, Denmark and the Netherlands.

Britain's government though, with perhaps the most serious economic distress of all, is holding firm. Despite strong criticism from some traditional Conservative supporters and a planned day of nationwide strikes Wednesday, Prime Minister Margaret Thatcher is still well ahead of her opponents in poll ratings, down only slightly from the peak of last spring's Falklands war.

Yet, a survey published earlier this month in the London Observer reported that one out of four British workers has been unemployed at some time in the past 12 months. The latest unemployment figure, announced today, is 3.34 million--14 percent of the work force--compared to about 700,000 a decade ago and barely a million when Thatcher came to office in 1979.

Other economic statistics are equally grim. Output is flat and actually declining if North Sea gas and oil are left out of the calculation. The Confederation of British Industry said in August that 78 percent of the country's manufacturing companies have less than four months worth of work on order. Imports are up much more sharply than exports, meaning that Britain is not finding the markets it needs abroad to bring unemployment down.

Nonetheless, the country's leading pollster, Market and Opinion Research International, reported yesterday that the Conservative support is at 47 percent of voters, with Labor at 37 percent and the alliance of Social Democrats and Liberals at 14 percent. All other major polls also find Thatcher's Tories in the lead.

The findings are all the more surprising considering that both the Confederation of British Industry and the Trades Union Congress, the equivalent of the AFL-CIO, have urged the government to take action immediately to boost the economy, giving relief to business and the struggling work force. Thatcher and her chancellor of the exchequer, Sir Geoffrey Howe, have resolutely refused.

Howe has been criticized widely for declaring the recession at an end several times in the past year only to confront new statistics that show the economy, as even current government appraisals acknowledge, "bumping along the bottom." With the next general election conceivably only a year away, the natural political response would be to start bringing the country out of its slump now to ensure the best possible public morale on voting day.

But Thatcher maintains that Britain's economy must recover on its own through continued improvements in productivity, a larger role for the private sector, greater competitiveness on world markets, innovative management and technological development. A government-induced upturn, she argues, would be illusory and ultimately leave the country worse off than now.

Three months after the end of the Falklands war, Britain's success in the conflict no longer represents a large factor in the government's continued strong showing. What seems to remain, political analysts generally agree, is a sense that Thatcher will not be deterred when she makes up her mind.

That determination -- "leadership in the truest sense" her supporters call it -- still appears to be working in Thatcher's favor.

On the economic front, Thatcher, like Reagan, points to a sharp drop in inflation and a lowering of interest rates as important gains for the economy for which she takes credit. These trends make the rise in unemployment less onerous to the public, officials say. After all, one senior government minister declared recently, "when you have 14 percent unemployment, that means 86 percent of the people are working."

Still, the government is vulnerable to pressure from its critics. Despite the various poll results with Conservatives comfortably in the lead, a solid majority of voters say they would support opposition parties in an election. The difficulty is that the opponents, for now at least, appear unable to project a feeling that the government is on the run.

Given the high unemployment rate, the trade unions should be especially active in battling the government. In fact, with jobs so scarce -- TUC membership has dropped by over a million -- strike actions are generally down. The next major test comes Wednesday when all the TUC unions have been urged to come out in support of pay claims by employes of the National Health Service who have been offered 6 percent wage increases by the government.

Thatcher is characteristically unrelenting. Last week, the day after the TUC's annual conference overwhelmingly called for the work stoppages on behalf of hospital employes, the prime minister convened her Cabinet for its first fall session, and let it be known that there would be no more money. Giving in to threats is not her style.