The opposition Labor Party scored a major victory in a parliamentary by-election held here yesterday, and hailed the vote as an indication that it can wrest national power from Prime Minister Margaret Thatcher's Conservatives in the next general election.

Results announced early this morning in the middle-class London district of Fulham, a formerly strong Labor seat that was swept into the Tory landslides of 1979 and 1983, gave Labor candidate Nick Raynsford a 44 percent plurality, with 16,451 votes.

The Fulham race -- necessitated by the death of its Conservative member of Parliament in January -- marked the first time in 29 years that Labor has taken a London constituency away from the Conservatives, and only the third such gain nationwide since 1971.

It comes during a period when Thatcher's popularity has fallen sharply due to rising unemployment and a widespread view of the Tories as internally divided and faltering.

A similar 44 percent showing throughout the country would put Labor within striking distance of control of Parliament, where the Conservatives now have an overwhelming 140-seat majority.

While the Conservatives were clearly disappointed with the 35 percent showing of candidate Matthew Carrington, Thatcher declared the results "typical" for a mid-term election, when a governing party traditionally is in a slump.

In what may be the most significant indicator of the direction the next nationwide poll will take, however, the Fulham vote appeared to bring the three-year winning streak of the third-party alliance of the Social Democratic and Liberal parties to a screeching halt.

The alliance has come in first or second in each of the 10 by-elections held since the last national race in 1983. But alliance candidate Roger Liddle ran a poor third in Fulham, with only 18.7 percent of the vote. "It is a disappointing result and there is no point in trying to pretend otherwise," Social Democratic leader David Owen said today.

Both Labor and the Conservatives had targeted the alliance as their principal enemy. With politics becoming more polarized here between right and left, the mainstreams of both main parties fear that the more centrist alliance will take votes away from them in a nationwide contest.

The Conservatives played down their defeat as a temporary one and the predictable result of "mid-term blues." It is possilbe that Labor's victory and the alliance's drubbing in Fulham are unrepresentative of what might happen in the next national election that could be as distant as two years away.

Nevertheless, many commentators here tended to characterize the Fulham race as having major political significance. This attitude is a reflection of widespread anxiety during a volatile political period here. Unprecedented direct-mail campaigning, high spending and appearances in the southwest London district by a wide range of leading figures of all parties were indications of the importance attributed to it.

Although Thatcher has had recent problems, Labor leader Neil Kinnock has had problems of his own and has not been able to capitalize on Thatcher's unpopularity.

Kinnock is engaged in a battle to distance himself from the party's left-wing. Last week, Denis Healey, a senior Labor statesman, told an Italian newspaper that Kinnock was inexperienced and that the party had not yet established "credibility as a party fit to govern."

Fulham gave Kinnock not only another parliamentary foothold on Labor's long climb back to power, but an important symbolic win at a time when he desperately needed it.