After a year of dramatic progress toward forcing a historic political realignment in Britain, the testing time has come for the new centrist alliance of the Social Democratic and Liberal parties.

Its popular support appears to have slipped for the first time since the alliance became the front-runner in public opinion polls as an alternative to the extremes of Prime Minister Margaret Thatcher's Conservative government and a more radical Labor opposition.

In closely followed polling by Market Opinion Research International, support for the alliance dropped from a peak of 44 percent last year to 34 percent in January, compared with 33 percent for the Conservatives and 31 percent for Labor.

Significant policy differences have surfaced among the Social Democrats, who divided three ways in a recent vote in Parliament on major Thatcher government legislation to curb trade union power. Questioned about this by a group of American businessmen here, coleader Shirley Williams said the party's leadership was spread across "a spectrum from moderate right-of-center to moderate left-of-center." Political analysts argue that the gap may become greater when the party is forced to take stands on other difficult issues.

Conflict between the Social Democrats and the Liberals also has been considerable over how to divide the country's 635 parliamentary constituencies for the next national election. Each is suspicious that the other is seeking a larger representation in Parliament.

The Social Democrats must choose a single leader this year and the alliance must select someone to offer as its candidate for prime minister. The man widely expected to become both, former deputy Labor leader Roy Jenkins, must first win a by-election in suburban Glasgow this spring for a vacant seat in Parliament.

The 78,000 voters who paid dues to join the Social Democratic Party during its first year also must approve a party constitution and settle disagreements left by a party conference here last weekend over how the leader should be chosen and how many women should be on the party's policy-making council.

The Social Democratic-Liberal alliance then must face voters across the country for the first time in local government elections in May, testing the significance of its dramatic victories in by-elections to fill vacant seats in Parliament and local councils.

The May elections "will be the key indicator of our support two years before the next national election," said Tom McNally, once an adviser to former Labor prime minister James Callaghan, who is now a Social Democratic member of Parliament.

Liberal Party leader David Steel told a group of American correspondents here that the local government elections would be "more signficant" than opinion polls, in which two of every five voters consistently supported the alliance until recently. He acknowledged the alliance could not form a government if it won much less than 40 percent of the vote in the next national election.

But Steel, who favors close cooperation between the Liberals and Social Democrats under Jenkins, said ideological splits in both the Conservative and Labor parties could lead to parts of them forming a centrist coalition with the alliance. Political analysts here continue to speculate most about a Conservative-alliance coalition in which Thatcher would be replaced as prime minister by a more moderate Conservative.

Yet some warn that Thatcher should not be counted out, despite the deep recession Britain has suffered since she became prime minister. Robert Worcester of Market Opinion Research International said his most recent poll had found a marked change in voters' expectations about the economy.

With the recession having bottomed out but recovery not yet clearly under way, 27 percent of those polled said the economy would improve this year while 40 percent expected it to get still worse. Two years ago, only 10 percent were optimistic and 74 percent, correctly, expected things to get worse.

Steel discounted the signs of improvement Thatcher supporters point to--fewer strikes, more moderate wage increases and greater productivity--as "the results of recession, unemployment and fears of bankruptcy."

"This has been achieved at a cost that is unacceptable to our society," he argued, "and that's why I don't think there will be a political recovery by the Thatcher government."