Opposition parties scored major gains in a series of local elections and two parliamentary races yesterday, dealing the governing Conservatives their harshest blow in Prime Minister Margaret Thatcher's more than 10 years as party leader.

Dissatisfaction with the government on social issues, including unemployment and education, along with opposition to Thatcher's support of the U.S. air raid against Libya, were cited by the winners as factors in the overwhelming Conservative defeat.

The government lost ground to the Labor Party -- which won more than 500 local council seats around the country from the Conservatives -- and the Liberals, who took one of the safest Conservative parliamentary seats and came within 100 votes of winning another.

With characteristic firmness, Thatcher said this morning that the results would bring no change in the substance or style of her government. "We're just keeping on with the policies, and redoubling our efforts," she told reporters. Party Chairman Norman Tebbit said it was "a natural tendency, midterm, for people to have a kick against the government."

Other Conservative leaders were less sanguine, and many publicly acknowledged that the results were far more disappointing than even their low expectations. They remain divided, however, over whether the solution to their problems lies in new policies or better presentation of the old ones.

Most galling to the Tories was the loss, due to a 19 percent vote swing from 1983 results, of the parliamentary seat in the staunchly conservative northeastern district of Ryedale to Liberal Elizabeth Shields. In the central district of West Derbyshire, another Conservative stronghold, the Tories held the seat by only 100 votes against a strong Liberal challenger.

On a local level, the Conservatives lost control -- primarily to Labor -- of 29 councils, most of them won in the 1983 general election that was a Thatcher landslide.

Labor Party leader Neil Kinnock said the results put his party "directly on course for a majority Labor government" when general elections are held within the next two years.

David Steel, whose Liberals operate in a third-party alliance with the Social Democratic Party, called yesterday "a massive vote of no confidence in the government and a massive vote of confidence in the policies we put forward."

The elections confirmed a trend away from the Conservatives in recent parliamentary by-elections and local races. They also conformed to opinion polls during the past 18 months that showed Thatcher steadily losing popularity to the point where the Conservatives, Labor and the alliance regularly share the vote in a three-way split.

Conservative commentators frequently point out that during seven years in office Thatcher has enjoyed wide swings in popularity but has been able to produce strong mandates when it counted. After her overwhelming 1979 victory, her ratings had fallen disastrously by 1981, when in a series of local elections the Conservatives fared nearly as badly as they did yesterday.

Those losses were made up in the 1983 general elections, when the Conservatives swept the boards with a massive parliamentary majority and substantial local gains.

But the 1983 victory is attributed in large part to widespread popular support for Britain's victory over Argentina in the Falkland Islands war. At the same time, the Labor opposition in 1983 was led by the left wing of the party under Michael Foot, providing an image of radicalism that gave the Conservatives a further advantage.

Also, the alliance, which had just come into being with the birth of the Social Democratic Party before the last general election, was a negligible factor at the time.

Much has changed since then. A popular war between now and the next nationwide race seems unlikely. Kinnock has made significant strides in softening Labor's image and making himself a more credible prime ministerial candidate. The alliance has won a significant portion of centrist voters weary of the traditional parties.

Still, many commentators believe that if the Conservatives lose power next time around, it will be due primarily to "the Thatcher factor." Although her strong convictions and unwavering policies helped put her in office, there are some signs that those qualities are becoming liabilities for the party and that the electorate is moving in another direction.