Shirley Williams, a leader of Britain's new Social Democratic Party, became its first elected member of Parliament today with a dramatically decisive by-election victory in what had been one of the safest seats in the country for Prime Minister Margaret Thatcher's governing Conservative Party.

Williams won 49.1 percent of yesterday's vote in the middle class suburban constituency of Crosby, just outside the port city of Liverpool in northwest England, to easily defeat Conservative John Butcher, who received 39.8 percent. Labor Party candidate John Backhouse was left with only 9.5 per cent and lost his election deposit.

The loss by such a large margin of a seat the Conservatives had held through eleven elections since the Crosby constituency was formed in 1948 represents the most serious political setback Thatcher has suffered since becoming prime minister in 1979. And the poor showing by Labor is the latest in a series of electoral humiliations it has suffered since being deeply divided by militant left-wingers demanding that its policies and leadership become more radically socialist.

Most significantly, Williams' victory is the biggest boost yet for the recently formed alliance of the Social Democratic and Liberal parties, which offers voters a centrist alternative to Thatcher's Conservatives on the right and Labor on the left. The alliance won its first parliamentary election just five weeks ago when Liberal William Pitt won another vacant, previously Conservative seat in the south London suburb of Croydon.

After the announcement early this morning that she had turned what had been a l9,272-vote Conservative majority in Crosby into a 5,289-vote Social Democratic majority, Williams said, "the election of the first Social Democratic Party candidate ever in this country is the beginning of a great movement of history, an idea that has found its time."

She predicted that the political momentum of the Social Democratic-Liberal alliance would eventually force the Thatcher government to modify its unpopular right-wing economic policies, and that the alliance would replace Labor as a major British party and sweep to victory in the next national election in l983 or l984. Williams called this "a crusade to save Britain from political extremism."

Liberal Party leader David Steel said the success of the alliance so far was far different from equally dramatic but historically isolated Liberal by-election victories of the Liberals in years past. "We now have a credible alliance," he said, "not a minor Liberal Party which was the repository for the mid-term protest vote."

Williams' victory gives the Social Democrats 24 members in the House of Commmons. Most of the rest of them had defected from Labor, one as recently as ten days ago. Three of the four founders and current co-leaders of the Social Democrats -- former Labor cabinet ministers Williams, David Owen and William Rodgers -- now have parliamentary seats. The fourth, former deputy Labor leader Roy Jenkins, who has been favored to become the sole leader of the Social Democrats, narrowly lost a by-election earlier this year in the northern England Labor stronghold of Warrington and is expected to try again when more seats are vacated by death or retirement.

With Pitt, the Liberals now have 12 members of parliament, providing the Social Democratic-Liberal alliance with a total of 36, the largest postwar third-party representation in the House of Commons. The Conservatives still have 336 seats, Labor has 245 and minor regional parties hold 16.

If the alliance can demonstrate it represents more than a passing protest against the current problems of the Conservative and Labor and hold the better than 40 per cent support it has been winning in opinion polls and parliamentary by-elections, it could win a majority in Parliament in the next national election or at least enough seats to become part of a coalition government.

If they win a share of power, the alliance parties are committed to changing Britain's voting system to proportional representation, which would make centrist, multi-party governments much more likely.

For the second time in as many months, the Crosby by-election campaign concentrated national media attention and an army of political celebrities on a suburban constituency with the kind of middle class voters who could well decide the next national election. It also provided those voters with a clear choice among the country's currently prevailing political philosophies.

Conservative candidate Butcher, a 39-year-old accountant, remained staunchly loyal throughout the campaign to Thatcher's survival-of-the-fittest free market economic philosophy and policies as the best way to get Britain moving again. Labor candidate Backhouse, a 28-year-old high school mathematics teacher, has just as openly supported his party's recently most radical policies of greatly increased government ownership of business, withdrawal from the Common Market and unilateral nuclear disarmament.

Williams, 51, stood on the Social Demcorats' comparatively bland support for Britain's current mixed economic, membership in the Common Market and nuclear arms reductions through international negotiation. She emphasized the Social Democrats' policy for reducing unemployment, a controlled increase in government spending on public works and job training programs that closely resembles policy changes Thatcher's Conservative critics have been urging her to make.

During the campaign, Williams also demonstrated her great personal popularity as the leading media personality of the new party. Although she holds some of the most radical political views of the party's collective leadership, such as favoring the abolition of all private schools, she showed an ability to appeal to voters as a warm, moderate politician.

She improved her position in the competition with Jenkins to become sole leader of the Social Democrats by beating him back into Parliament. Jenkins had resigned his seat to serve a term as president of the administrative commission of the European Common Market, while Williams lost hers during the Conservatives' national election victory in l979.