The partnership of Britain's new Social Democratic Party and the older Liberals, which only a year ago seemed poised to radically reshape the country's politics, began a concerted effort today to capture again that short-lived spirit of expectant glory.

The Alliance, as it is formally known, strutted its best stuff at a round of national press conferences climaxing in a large London rally tonight featuring the party leaders, Roy Jenkins for the Social Democrats and David Steel for the Liberals. The aim, as Jenkins acknowledged, is to place themselves "more strongly in the public eye."

"It has been very difficult," said Steel underlining the point ruefully, "to fight our way back since the Falklands."

Although the Alliance slide began before the war in the South Atlantic--from a peak of 52 percent support in the polls as 1982 began--the crisis gave Prime Minister Margaret Thatcher and her Conservatives a hefty boost, which has since been maintained. Thatcher's trip to the Falklands last week and publication of a major report absolving her government of blame for not preventing the conflict have apparently enhanced her standing.

A Gallup Poll published this morning showed that if a ballot were held now, the Conservatives would get 44 percent, the Labor Party would get 31.5 percent and the Alliance 22.5 percent--figures that again lengthen the Conservative lead over the opposition and show the extent of the Alliance's continued decline.

But Alliance supporters believe that Thatcher's dominance of British politics is not immutable. In their view, the serious weaknesses of the economy must eventually make her vulnerable. In particular, Jenkins said today, the prospect is that in June, the earliest likely date for an election, unemployment now at nearly 14 percent will be "no better or maybe worse" and inflation will again be rising.

"I don't believe the position of the government will look good in six months," Jenkins asserted. He conceded, however, that political prognostications in Britain since the last election in 1979, including those predicting that the fledgling Social Democratic-Liberal alliance were on the way to "breaking the mold," have all been proven wrong.

The Alliance's problems go somewhat deeper than the special circumstances of Thatcher's personal sway of the moment. When a group of leading Labor moderates, including Jenkins, David Owen and Shirley Williams abandoned their increasingly left-wing party in the spring of 1981 to form the Social Democratic Party, the move created enormous excitement about a basic realignment of British politics, creating a strong new center.

The defection of about two dozen members of Parliament (even one Conservative joined), the public affiliation of scores of prominent figures and several early electoral victories provided dazzling momentum. But differences emerged between those who favored a tight partnership with the Liberals and those preferring a clearly separate identity for the Social Democrats.

While the two parties continued to contest local elections and held two party conferences last fall, they have grown steadily closer in fact and in the public mind. The trend was accentuated last July when Jenkins defeated Owen for the party leadership.

The parties spent months dividing up the country's 600-plus parliamentary constituencies so that in the next election they will field one candidate for each seat. The process created considerable bickering among local groups that further dissipated the Social Democrats' image as a bold new force in British life. In the end, many commentators wrote that the Liberals had gotten the majority of seats where the Alliance stood a chance of winning.

On policy, the Social Democrats issued a stream of position papers carving out a middle economic ground between Thatcher's monetarism and Labor's socialism, but the party did not emerge vividly linked with any single issue. Even on defense where the more dynamic Owen is principal spokesman, the party's stand on whether cruise missiles should be deployed in Britain is to wait for more developments in the Geneva negotiations.

The Social Democrats have become "a junior member of an alliance with the Liberals who haven't come close to winning an election in 60 years," said one early but now disillusioned member of the party.

The gloomiest forecasts are that if only a handful of Social Democratic candidates wins parliamentary seats, the party, like other breakaways in the British past, will be absorbed into the Liberals or a revitalized Labor Party. But Steel, at 44 the youngest top party leader, is confident that the Alliance, with both its parts, will make a strong, enduring mark.

The record of Liberal showings in recent elections has been to do better than poll figures predict by at least 25 percent, Steel said today.