Prime Minister Margaret Thatcher's Conservative Party won a strong vote of confidence for her government's handling of the Falkland Islands crisis in local government elections in Britain yesterday.

Politicians from all parties said the Conservatives did better than the national government party has in any mid-term local elections since World War II because of voters' support for the government in the conflict with Argentina over the Falklands.

It also appeared from election results still being tabulated this morning and a new national opinion poll published today that Thatcher's government lost only a small proportion of this support after the sinking of an Argentine cruiser and the destruction of a British destroyer caused the conflict's first large-scale casualties.

This is expected to strengthen Thatcher's hand as her "war cabinet" of senior ministers decides on Britain's next military and diplomatic moves.

Thatcher has been under conflicting pressures in recent days. Conservative hawks in Parliament have been pressing Thatcher to move as quickly as possible to invade the Falklands and bomb bases on the Argentine mainland. Others, including some members of her Cabinet, have been cautioning Thatcher to avoid further military escalation before exhausting every remaining diplomatic channel.

A leading academic political analyst here, Ivor Crewe, called yesterday's local government elections "an extraordinarily good result for the Conservatives, which has to have a great deal to do with the Falklands crisis."

A computer projection by BBC television from a sampling of city and district council constituencies across the country showed the Conservatives winning 39 percent of the vote, compared to 32 percent for the opposition Labor Party and 26 percent for the electoral alliance of the Social Democrats and the Liberal Party. This is in line with the most recent opinion polls here, and represents a strong recovery for the Conservatives from their position in the polls a year ago.

In a national parliamentary election, according to the BBC projection, yesterday's result would give the Conservatives 315 of the 635 seats in the House of Commons, compared to their majority of 334 seats now. Labor would win 266 seats, the Social Democratic Liberal alliance only 30 and minor regional parties 24.

The Conservatives appeared to match the support they won as a resurgent opposition party in the last elections for the same local councils in 1978, which foreshadowed the Conservatives' national election victory the next year that produced the Thatcher government.

Conservative Party chairman Cecil Parkinson, who as paymaster general participates in Thatcher's Falklands crisis Cabinet of senior ministers, said, "Our vote is holding up well. We have retained seats won in the boom year of 1978, and added to them. These results are a firm endorsement of the determined leadership of Margaret Thatcher, not only over the past few weeks, but over the last three years."

"People feel the government is handling things well," said another member of Thatcher's Cabinet, James Prior. He attributed yesterday's "remarkably good result for the government" to both confidence in its handling of the Falklands crisis and a recovery of voter support for Thatcher's economic policies now that Britain's worst recession in a half century appears to be ending.

One of the Social Democrats' four co-leaders, William Rodgers, said, "The Falklands factor is a major one" in the disappointing showing of his party. It won five fewer council seats than it expected in large metropolitan areas like London and Birmingham. Many of the council members across the country who defected from Labor to the Social Democrats during the past year lost their seats, including all 26 defectors from Labor in the London borough of Islington.

Although the Liberals did better, the Social Democratic-Liberal alliance polled only two-thirds as many votes as opinion polls indicated they might win just a few months ago. The alliance suffered during the local election campaign from being pushed off Britain's front pages by the Falklands crisis and the fact that the issue concentrated national attention on Thatcher and opposition Labor leader Michael Foot.

The Labor Party, which has become divided over the Falklands crisis, with many of its left-wingers demanding an immediate cease-fire by Britain, barely held its own in many traditional urban strongholds. It lost the city council of Birmingham to the Conservatives, a major defeat in Britain's second-largest city. Birmingham Labor Party leaders attributed it mostly to the Falklands crisis.

A new national opinion poll by the Markets Opinion Research International firm here, published in The Economist magazine today, shows that public support for Thatcher's Falklands' strategy declined slightly after recent Argentine and British casualties. But 71 percent of the respondents, who have been polled four consecutive weeks on the Falklands crisis, said they were still satisfied this week with Thatcher's handling of the crisis, down from 76 percent last week.