Social Democrat tries for Parliament - and party leadership

Roy Jenkins, former deputy leader of the British Labour Party, has resumed his battle to re-enter Parliament under the banner of the Social Democratic Party (SDP).

He is being given a good chance of winning a by-election in the Scottish seat of Glasgow Hillhead and thus of strengthening his claims to ultimate leadership of the recently formed party.

Jenkins, who was president of the European Commission in Brussels until a year ago, took a hard look at Hillhead before offering himself as candidate of the SDP-Liberal Party alliance.

His basic fear - that the Scots would not be prepared to accept an English carpetbagger with an ''Oxbridge'' accent - has already been answered by clear signs that the Glasgow middle class is flattered to have him in their midst. His industrious and articulate campaigning seems to be making a favorable impression.

Last summer Jenkins was narrowly defeated at a by-election in the English seat of Warrington. This time, he is determined to win - and take the seat away from the Conservatives, who won it at the 1979 general election.

Three months ago another SDP luminary, Shirley Williams, returned to the House of Commons, soundly beating her Labour and Conservative opponents at Crosby. That left Jenkins as the only member of the so-called ''gang of four'' that founded the SDP still lacking a parliamentary seat.

Hillhead is a vital struggle for the SDP-Liberal alliance. If they can win, they will demonstrate their political strength against all major parties, including the Scottish Nationalists who will be contesting the seat.

The Labour Party, badly torn by internal ideological struggles, is fielding a candidate with little chance of heading off an SDP-Liberal alliance victory.Labour's flag-bearer is a left-winger sympathetic to the cause of Tony Benn. The Tories are still preparing to choose a candidate.

To clinch the alliance nomination, he had to beat off an attempt by local Liberals to field their own man - an indubitable Scot - in his place. After much wrangling, Jenkins gained the nomination.

The Liberals won an SDP promise that they would be able to contest a choice seat the moment one comes vacant.

The alliance, however, is beginning to look decidedly uneasy. As selection of a candidate for Hillhead proceeded, the Liberals and Social Democrats clashed publicly, with the Liberals claiming that their partners were attempting to bully and pressure them.

If the alliance is to have a chance of proving its claim to be a ''new force'' in British politics, it must hold together and sink its differences.

The Hillhead by-election is scheduled to take place some time in March.