The challenge of putting their almost identical, radically conservative economic philosophies to critical political tests in the coming months is expect to override the usual summit meeting discussions of world affairs when British Prime Minister Margaret Thatcher visits President Reagan here this week.

Reagan's advisers believe they have only a few months of postelection mentum in which to begin making the unprecedented cuts in federal spending, taxing and regulating they think can reduce inflation and free the stalled American economy from the shackles of big government.

Thatcher, who has spent nearly two years trying to force a similar reconstruction of the badly battered British economy, also sees the next six months as a crucial "test of will" for her own survival-of-the-fittest tight money, budget-cutting strategy for reducing inflation, inefficiency and the size and economic involvement of government.

As Britain's deepest postwar recession hits bottom, with industrial production plummeting and unemployment soaring at rates last seen during the Depression, fears are growing that Thatcher's medicine may be permanently disabling rather than curing. If the social and political damage appear too great during the coming dark months before recovery from the recession finally begins, Thatcher could be forced by her own Cabinet or Conservative Party to drastically change the prescription or be placed as party leader and prime minister.

Reagan and Thatcher are expected to give each other plenty of encouragement during her three days here. British and American officials are expecting a "love feast" of mutual admiration for each other's free enterprise evangelism at home and staunch anti-communism abroad. A senior American diplomat said Thatcher "can expect a very sympathetic audience for whatever she wants to say."

But in confrontations with American journalists and in an unusual meeting at the British Embassy with American business executives, congressional leaders and Reagan administration economic strategists, she will face questions about what has gone wrong in Britain and whether Reagan's policies risk the same dire fate as hers.

The package of budget and tax cuts Reagan announced Wednesday -- coupled with his administeration's attack on government regulation and the high interest rates Federal Reserve Chairman Paul Volcker is using to discourage borrowing, slow the growth of the money supply and squeeze down inflation -- is remarkably similar to Thatcher's approach. In a radical departure from postwar governments in Britain and the United States, Thatcher and Reagan have renounced the use of government money and power to spur economic activity and bring about social change.

Thatcher is cutting spending on subsidized housing, education, local government, unemployment and some welfare benefits and public works -- just as Reagan wants to do. She also is reducing the number of government employes and, belatedly, trying to hold down their pay increases -- just as Reagan intends.Her government is even experimenting with "urban enterprise zones" where red tape would be cut to attract enterprises to dying inner city areas at relatively little cost to the government -- just as Reagan proposes doing.

Thatcher also sought, like Reagan, to reduce the income tax bite on middle and upper income people, believing it would encourage them to work harder, save and invest more money to help get the economy moving again. The recession's drain on government revenue has forced her to postpone real relief for the majority of Britons, whose total tax burden actually has increased under Thatcher.

The best-paid Britons have benefited some, but there is no sign that they have ploughed their extra money back into the sagging economy.

Just as Reagan expects a psychological boost from his policies for the ailing American economy, Thatcher had similar hopes for Britain. But the growing crisis she inherited when she became prime minister nearly two years ago has only gotten worse.

Britain's manufacturing production during the last three months of 1980 fell by 14 percent from the same period in 1979 -- the worst slump since the 1930s. Even counting Britain's North Sea oil bonanza, industrial production dropped 9 percent -- pulling the British economy back 13 years, to levels of 1967.

Unemployment has burgeoned to 10 percent of the British labor force -- another post-Depression record -- and is still rising rapidly.

Thatcher's Conservative Party still has a 43-seat majority in Parliament and does not have to contest an election until 1984. But a significant number of her Cabinet ministers and Conservative members of Parliament are increasing worrying about possible long-run social and political damage from her policies.

Despite little evidence of social unrest, there are fears that a nationwide strike by miners, water workers or civil servants -- all possibilities in the coming months -- could cause Thatcher serious trouble.

Although the opposition Labor Party is suffering from a debilitating ideologically split following a lurch to the left, Thatcher's government has recently lost ground badly in opinion polls. And a dramatic impact has been made by a social democratic party breaking away from Labor.

The new party grouping seeks to capture the center of British politics by offering to protect Britain's mixed economy and postwar welfare state from both Thatcher's dogmatic free-market determinism on the right and Labor's increasingly militant state socialism on the left.

When asked about this, Thatcher admits mistakes, including moving more cautiously than intended on government spending and pay. She also points out that she began her experiment with a weaker economy at a worse time than Reagan.

She recently told a group of American correspondents in London that Reagan was fortunate not to be confronting the beginning of a world recession, a sharp increase in oil prices and the rapid decline of expensively subsidized nationalized industries as she did nearly two years ago.

Thatcher recently has departed from her strategy to accommodate reality by giving more money to slimmed-down, government-owned auto and steel industries, and increasing spending on training and job creation programs for the growing number of unemployed young adults.

Explaining these "adjustments" to Parliament recently, Thatcher's new leader of the House of Commons, Francis Pym said, "The simple truth is that in the light of the deterioration in the world and domestic economic framework, we could neither press ahead regardless with our planned schedule nor avoid some much-needed measures to deal with some of the distressing effects."

But Thacther continues to insist that she will not depart significantly from her course and that ultimately she will be successful. She contends she is already accomplishing her primary goal of reducing inflation.

After Britain's inflation rate doubled to nearly 22 percent in Thatcher's first year in office, it has fallen to 13 percent and is expected to drop below 10 percent this year.

A growing number of independent analysts also agree with Thatchter that much of British industry has been forced by the recession and her policies to slim down drastically and become more efficient.

If Thatcher can make it through the critical months ahead as the recession bottoms out, she will benefit from the resulting, if slow, upswing as well as from a dramatic growth in government revenue from North Sea oil expected to begin about 1983.

That should enable Thatcher to realized her ambition of real reductions in Britons' tax burdens to spur new economic activity. But it would not guarantee that a more modern, revitalized British economy would emerge and prosper without a permanent high level of unemployment that would violate all postwar British social and political aspirations.

"The jury is still out," observed the outgoing American ambassador to Britain, Kingman Brewster, in an interview in London. "If it works, it will come together in 1982. That's when there should be a change of direction in unemployment and economics growth."