The only good news for Britain's battered economy is that the country's deepest recession since the Great Depression of the 1930s should bottom out this year.

In the process, 1981 is certain to be a very painful year for many Britons, and a politically trying one for Prime Minister Margaret Thatcher and her wobbling monetarist, survival-of-the-fittest strategy for coping with the crisis.

In recent public-opinion polls, Thatcher's Conservatives have fallen more than 20 percentage points behind the opposition Labor Party, which under its new, more militantly socialist leadership wants to return to expanding the welfare state and increasing government intervention in the economy.

Thatcher's government relaxed its monetarist policies slightly late in 1980, especially by reducing the minimum lending rate from 16 to 14 percent. But it still is trying to cut government spending while having to pay out much more in unemployment benefits. And it is being forced by the recession's impact on government revenues to increase taxes. These steps are expected to continue bleeding an already anemic economy.

Britain's industrial output will continue to decrease markedly in 1981, with more factories closing, more businesses collapsing completely and hundreds of thousands more jobs lost. The gloomiest independent forecast, by the International Organization for Economic Cooperation and development, predicts that unemployment in Britain will continue to rise rapidly from one of the highest rates in history -- more than 9 percent at the end of 1980 -- to nearly 12 percent. This would mean more than 3 million jobless workers -- numerically if not proportionally as many as during the 1930s.

Exports are expected to fall off sharply because of the worsening recession elsewhere in Europe and the increasing uncompetitiveness of British goods on the world market. Their comparative prices have been driven up by nearly 50 percent since 1978 by increases in production costs and the high exchange value of the British pound sterling, kept up by the bankability of Britain's one certain economic asset -- North Sea oil.

One beneficial byproduct of the severe recession and Thatcher's policies has been a steady decline in the inflation rate, which should continue through 1981. It has fallen from a peak of 22 percent in mid-1980 to just over 15 percent and is expected to drop about 10 percent within a year.

Imported materials and products cost less because of the high exchange rate of the pound sterling, and hardpressed British businesses have been forced by the enconomic crisis to keep prices down and pay workers less. Thatcher's government also is trying to hold down pay raises in the government and the nationalized industries. Last year those raises averaged more than 20 percent; this year the government hopes to keep them to about 10 percent.

Surviving business also have been forced to tighten their belts and increase productivity, although no lasting national productivity improvement is yet discernible because total production continues to plummet. Austerity also has dangerously decimated profits and discouraged new business investment, which likely will slow and limit the extent of the economy's recovery, now expected to begin in 1982.

Thatcher has been forced to ask the country once again to patiently endure at least one more year of things getting worse before getting better.

It also is expected to be a year of belt-tightening in the much richer Scandinavian countries across the North Sea.

Ironically, Denmark's socialist government of Prime Minister Anker Jorgensen is being as Draconian as Thatcher in tightening money, forcing down the standard of living and deflating the Danish economy -- which has been depending far too long on borrowed money. Its gigantic trade and government-budget deficits had threatened to bankrupt the country.

But Jorgensen's government acted during 1980 to steeply increase taxes on energy and consumption and slow the growth of both government spending and the money supply. Denmark's monetary base is contracting, inflation is falling and Danes are being forced to accept a loss affluent life style. Both disposable after-tax income and consumption have decreased by nearly 5 percent and are expected to continue falling.

Those measures also mean fewer welfare-state social benefits for better-off families and more unemployment -- both sharp contrasts to the post war trend in Denmark. The unemployment rate is expected to continue rising dramatically to 8 percent in 1981 and nearly 10 percent by 1983. New "social income" criteria to limit welfare-state benefits -- such as unemployment compensation and child allowances for high-income families -- are part of a drive to stop government spending from increasing faster than the inflation rate in the early 1980s.

Svend Andersen, a governor of the Danish Central Bank, believes the previously profligate Danes' attitudes are being changed by the economic crisis."People are no longer so willing to go into debt," he said. "What we are doing was necessary, but it also has not been uncourageous. There are some complaints, but Denmark's position is better than a year ago."

Both the budget and balance-of-payments deficits remain large, however, because of the enormous interest payments on money borrowed to cover past deficits and Denmark's dependence on expensive imported oil.

This may be the year when Sweden also faces the necessity of tackling similar problems. The contraction of its traditional manufacturing industries, particularly shipbuilding, are making it more difficult for the private economy to support the Swedish welfare state's public sector, which consumes 65 percent of the country's gross national product and accounts for 40 percent of its jobs.

Despite holding just a one-vote majority in parliament, the right-of-center coalition government has begun what it promises will be annual rounds of spending cuts during the 1980s. Business and housing subsidies are to bear the brunt this first year, but spending for welfare-state social services may eventually have to be trimmed. The value-added sales tax also has been increased to 23.5 percent, the highest in Europe, to help cut the government's budget deficit.

Norway, with its burgeoning North Sea oil income (proportionally much larger than Britain's because Norway's population is one-tenth the size), and Finland, with its assured trade with the Soviet Union, expect brighter years in 1981. But to fight inflation in both prices and wages that could stunt their more robust economic growth, their governments and central banks also intend to pursue restrictive fiscal and monetary policies that could, in Finland at least, significantly increase unemployment.

So even after the cold Nordic winter ends, it could still be a chilly year in Scandinavia.