Britain's Social Democrats hang on a by-election

The result of a by-election in the Scottish city of Glasgow March 25 may set the tone of British politics for the next two years.

That is the view of seasoned observers who are trying to decide whether Roy Jenkins, a former Labour Party deputy leader and now a luminary of the new Social Democratic Party (SDP), will win the seat of Hillhead.

If he succeeds, the SDP, born just over a year ago, will remain a potent force in politics. If he fails, the breakaway party expects to face acute problems of credibility with the British electorate.

Hillhead is a strange place for such a vital contest to be held. The seat has been in the Conservative Party fold for many years. It has working-class sections, but it is mainly middle class, and in Scotland that means voters keep their own counsel and are notably resistant to brash blandishment by ambitious politicians.

Jenkins is not brash, but he is not Scottish, either. He is a man of working-class origins but upper-class habits, fond of good living, decidedly English in manner of speech. Some Hillhead voters have been suspicious of him from the start.

But for the man who nearly won another by-election, in Warrington last year, the Tories and Labour have made a mighty effort to head Jenkins off. Helped by an annual budget earlier in the month geared to middle-class interests, the Conservative candidate has argued that inflation is falling and maintained that the SDP is a ''media creation.''

The Labour Party, beset by internal splits, has sent left- and right-wing spokesmen to Hillhead and argued that Conservative government has meant high unemployment for Britain, and particularly Scotland.

In the last two weeks of the campaign some of the emphasis shifted to the government's decision to adopt the Trident II missile as Britain's future nuclear deterrent. Trident will be based in Scotland, and the Tories believe this is a persuasive argument for rejecting Labour and the SDP, both of which have attacked the Trident decision.

Jenkins has proved the most industrious and subtle campaigner in the by-election campaign. He knows that if he loses, his political career will probably sustain a fatal blow.

He is seen as the person most likely to lead the SDP into the next election - if the party wins Hillhead. If he should fail, there would almost certainly be a bruising leadership contest between David Owen, a former Labour Foreign Secretary, and Shirley Williams, a former Labour Cabinet minister who convincingly returned to Parliament after a by-election late last year.

The SDP badly needs a fillip to its fortunes. After its confident launch last year, the party has begun sagging in nationwide opinion polls. The time for renewal of individual membership subscriptions is about to arrive, and without a success at Hillhead many existing supporters may fall away.

Tories and Labour realize that Hillhead is a vital seat because it could end their duopoly of political power in recent decades. Indeed, some observers say neither party cares who wins, so long as it is not the SDP.

The Social Democrats are fighting Hillhead in alliance with the Liberal Party. If the SDP goes to Jenkins, the alliance will be greatly strengthened and the two parties will begin planning their joint strategy for the general election that must be held in the next two years.

One unpredictable factor in the Hillhead result may turn out to be the Scottish National Party. Its candidate has been trailing the other three by a considerable margin.

As polling day approached, the three main candidates were all forecasting that they would win, though observers in Scotland noted that the Jenkins camp was couching its optimism in modestly chosen words.

Jenkins, shrewd campaigner that he is, believes modesty is still a valued attribute in Scotland, particularly for an English-accented, Welsh-born former Labourite who happens to have staked his career on a seat north of the border.