After a year of severe recession, factory closings and rising unemployment, most Western European countries expect to begin a gradual economic recovery in 1982. Analysts forecast at least some increase in gross national product for nearly all of them after stagnation and decline in 1981.

But the recovery is not expected to be sufficient to prevent a further big increase in unemployment, according to most analysts, and may not be able to survive a serious downturn in the United States. It also will leave most Western European economies with still serious structural problems and their governments with big budget deficits.

The most rapid expansion in 1982 is expected in France because of a big boost in government spending by President Francois Mitterand's Socialists, a notable departure from efforts almost everywhere to curb public expenditure. West Germany, taking advantage of lower competitive export prices because of the strength of the dollar, is expected to lead the less dramatic upswing elsewhere.

To a great extent, the Europeans will only be making up some of the deficit in growth they have suffered the past two years. The question will be whether the recovery can be sustained later into the 1980s.

Britain, whose recession has been deeper and longer than that of any other western industrialized nation, is expected to continue lagging most of its Common Market partners. Its forecast of expansion of one or 2 percent in 1982 would still leave its annual output well below the level of 1979, when Prime Minister Margaret Thatcher took office.

For Western Europe's smaller welfare state societies, such as Belgium and Denmark, the recovery may well not be sufficient to rescue them from chronic economic and political crises caused by their inability in recent years to keep up with the cost of their large, high-wage public sectors. Their governments are resigned to trying to curb government spending and hold down wages while somehow expanding their private sectors through exports.

Most of the European economies also are still plagued by unsolved structural problems caused by the failure of large, traditional industries like automaking, shipbuilding and steel to compete successfully with more efficient Japan and lower-wage countries in the Third World. Further painful adjustments will have to be made this year.

The closing of more large factories and the rapid growth of the working-age population produced by a baby boom in the 1960s means that this year's expected economic upturn will not stop a steep rise in unemployment that already has become Western Europe's most important economic, social and political problem.

The numbers of workers without jobs is forecast this year to top three million in Britain, two million each in France and Italy, and more than 1.5 million in West Germany--levels unseen since the Depression of the 1930s. The cost of unemployment benefits alone has become a major problem for governments trying to reduce runaway budget deficits, and diverts money that could otherwise be channeled into economic expansion.

The political price of high unemployment figured last year in dramatic changes of government in France, Greece and Norway, the weakening of Chancellor Helmut Schmidt's government in West Germany and the difficulties in forming governments in Holland, Belgium and Denmark. Voters in Sweden get their turn in 1982, and the fate of the Thatcher government in 1983 or 1984 elections may well depend on economic progress in Britain this year.

Except for the stimulation of government investment in France, the key to the year's economic fortunes for most Western European economies is the competitiveness of their exports on a world market that is not expected to expand very much. Besides West German dependence on its relatively more efficient industry and the lower exchange value of its currency compared to the dollar, a number of other countries are banking on steps taken during the recession to improve their competitiveness.

Sweden, for example, expects to benefit from a 10 percent devaluation of its currency last September, which makes prices of its exports relatively cheaper. The Danish government has forced a drastic reduction in living standards on its workers to curb the rise of production costs. The Thatcher government is counting on the increased efficiency of British industries that have had to shed thousands of workers to stay in business.

To some extent, the year will test the relative economic philosophies behind the belt-tightening in much of Europe, symbolized by Thatcher monetarism, on one side, and Mitterrand's decision to reverse course and spur recovery with increased government spending on the other. As Thatcher has frequently pointed out, Mitterrand is benefitting from the relatively small past budget deficits resulting from the tighter fiscal policies of his predecessor.

It is also expected to be year of continuing tension within the European Common Market and between it and the United States and Japan over export policies for highly competitive products like steel and automobiles. Analysts warn of trade wars that could do more damage to the NATO alliance than disputes over foreign policy issues like Poland, or of disagreements within Europe over agricultural and industrial subsidies that could tear apart the Common Market.