Britain's Social Democrats: what goes up . . . ?

Britain's Social Democratic Party (SDP) has been celebrating its first year amid growing indications that its initial buoyancy is beginning to sag.

Only three months ago popular opinion polls showed that the SDP and its Liberal Party allies together were far ahead of the Conservative Party and the Labour Party in public esteem.

But suddenly a new set of polls has suggested a sharp slump in popular enthusiasm for the SDP-Liberal alliance.

In November, the alliance was 10 points ahead of Prime Minister Margaret Thatcher's Conservative Party. Now they are only 1 point ahead.

This downward trend follows a series of disputes between the Liberals and the SDP over selecting candidates for parliamentary and local authority elections.

Further concerns for the SDP include infighting by its original leaders, or the ''gang of four,'' over who should be leader and what policies should be followed.

The latest disruption has been caused by a leadership split on whether to back the Thatcher government's tough new employment bill, which includes provisions to curb trade-union power.

One section of SDP parliamentarians announced that they would support the bill in Parliament. Others, including Shirley Williams, voiced the fear that backing the bill would alienate trade-union support.

Political analysts are noting that in the drastic fall in popular support for the alliance, those who are deserting are returning to both the Conservative and Labour parties, with the governing party getting most of the benefit.

Officials of the Conservative Party central office are claiming that the SDP-Liberal alliance enjoyed a public relations boom in the early months, but that now voters are reverting to traditional patterns.

Tory supporters are also suggesting that Mrs. Thatcher is having some success in returning Britain to sustained economic growth and that the public is acknowledging this.

With the unemployment figure now over 3 million and still rising, the argument that the government has regained an economic grip looks thin.

A more convincing reason why the SDP-Liberal alliance is flagging is its own failure to settle down into a friendly working relationship. There have been sharp arguments, highly publicized in the media, about who should stand for particular seats.

Liberal Party leader David Steel has had difficulty keeping his supporters in line. Some still argue that the Liberals should eschew cooperation with the SDP.

An insistent cry among critics of the alliance is that it is, upon close inspection, essentially a middle-class creation with no working-class roots.

The deputy-leader of the Labour Party, Denis Healey, hammered this criticism home in analyzing the alliances's reason for deciding to support the employment bill, which limits the closed shop.

Healey argued that a party really determined to acquire a large following in Britain was bound to resist the employment bill.

It seems clear that the SDP made a major error in not moving quickly to establish a firm leadership structure with one person assuming leadership.

Roy Jenkins, currently engaged in trying to win the Hillhead parliamentary seat in Glasgow, is the favorite to become leader of the SDP, but David Owen and Mrs. Williams are also candidates.

This coming weekend the SDP will meet to consider its constitutional structure. But a more insistent question to be answered is why the party seems to be losing popular support.

If the present downward trend continues the SDP-Liberal alliance might have trouble winning more than 40 seats at the next general election - massively below what the ''gang of four'' were forecasting only a few weeks ago.