Britain's Conservative Party, continuing to profit from strong voter support for Prime Minister Margaret Thatcher's conduct of the Falkland Islands war, yesterday won its first parliamentary special election in more than two years.

After four consecutive losses--the last three to the new centrist electoral alliance of the Social Democratic and Liberal parties--the Conservatives easily won the vacant parliamentary seat in the staunchly Tory, upper middle-class suburban constituency of Beaconsfield, west of London. Oppostition politicians blamed the Falklands crisis for the strong showing of the Conservatives' candidate, H. Timothy Smith, who had campaigned as a supporter of Thatcher's conduct of the war.

With all the ballots counted early this morning, Smith, a 34-year-old Oxford-educated accountant, won 62 percent of the vote, even better than the 60 percent gained in 1979 by veteran Conservative Sir Ronald Bell, whose death created the vacancy. The candidate of the opposition Labor Party finished a poor third with just 11 percent, down from 20 percent three years ago.

The Liberal Party candidate of the year-old alliance of the Social Democratic and Liberal parties finished second with 27 percent, an improvement on the 17 percent Liberal share in 1979, but behind recent showings for the newly formed bloc, which has suffered from the Conservatives' upward surge during the Falklands crisis.

The latest national opinion poll, conducted Tuesday and Wednesday by Market Opinion Research International for Friday's edition of The Economist magazine, showed another significant increase nationwide in voter support for the Conservatives. Asked which party they would vote for if a national election were held now, 51 percent of the respondents chose the Conservatives, compared with 38 percent of the same sample polled about four weeks ago.

Support for the Labor Party fell to 25 percent from 32 percent at the beginning of May. The Social Democratic-Liberal alliance slipped to 22 percent from 28 percent at the beginning of May and more than 40 percent just six months ago.

For the first time in Market Opinion Research's 14 years of polling, according to its director, Robert Worcester, the Conservatives now lead the other parties among voters aged 18 to 24 and among skilled workers, who constitute a third of Britain's voters. The new poll records 84 percent voter satisfaction--rising to 96 percent among 18- to 24-year-olds--for Thatcher's handling of the Falklands crisis.

Other polls by the Gallup and Opinion Research organizations here show similar sharp rises in support for the Conservatives, with the Social Democratic-Liberal alliance falling from first to third among the major British parties during the last several months.

Worcester, a leading political opinion analyst here, said it was likely that the Conservatives would lose a significant amount of their new support if Britain failed to win the Falklands war or if the country's attention shifted back to its entrenched economic problems after a military victory. He said he doubted that Thatcher would call a quick national election this autumn, a year and a half before the end of her government's five-year term, because "the British electorate would resent and resist blatant exploitation of military success."

However, he said, Thatcher might move "after a decent interval," perhaps as soon as the spring of 1983, to take advantage of a Falklands victory, the recent reduction of inflation to below 10 percent, signs of a gradual recovery from Britain's severe recession and parliamentary redistricting expected to benefit the Conservatives.

Worcester and other political analysts here said the new Social Democratic Party, which was riding high just a few months ago after strong showings in parliamentary by-elections and in opinion polls, now faces a fight for survival.

After being displaced from newspaper front pages by the Falklands crisis, it fared badly in local government elections earlier this month, while its junior electoral alliance partner, the venerable Liberal Party, did considerably better, because of its established local party machinery. Of the four current coleaders of the Social Democrats, only Labor former foreign secretary David Owen has remained in the public eye during the Falklands crisis with frequent statements in Parliament and on television and radio generally backing Thatcher's overall strategy.

Owen is not given a much better chance than before to become the first elected single leader of the Social Democrats in national balloting next month by paid party members. The early favorite, Roy Jenkins, a former deputy Labor leader and European Community Commission president, has largely disappeared from public view since returning to Parliament with a come-from-behind special election victory in a middle-class Glasgow constituency in late March.