Britain's longest and most violent strike ended today, when coal miners' delegates here voted 98 to 91 to return to work Tuesday despite having failed to reach a settlement with the state-run National Coal Board.

The vote to end the yearlong strike went against the recommendations of the executive committee of the 186,000-member National Union of Mineworkers and its fiery leader, Arthur Scargill, who has been the strikers' driving force.

But the delegates voting represented proportionally the entire membership, and the result is likely to be viewed as a victory for the Conservative government of Prime Minister Margaret Thatcher. She expressed "overwhelming relief" with the result, saying, "We had to make sure that violence and intimidation and impossible demands could not win."

A 1974 strike by the miners' union, traditionally one of the most powerful in Britain, had contributed to the downfall of the Conservative government of Edward Heath.

Public opinion polls have indicated that Britons are strongly dissatisfied with the performance of all three key figures in the strike -- Thatcher, Scargill and the coal board chairman, Ian MacGregor. The labor struggle took a political and social toll in addition to its considerable cost to the economy.

There were angry scenes outside the Trades Union Congress conference hall as Scargill, 46, emerged to announce the dramatic decision. Several hundred miners shouted abuse at the delegates. Cries of "No, no" went up from the miners. "We are not going back," shouted one striker, while another yelled at Scargill, "Traitor, you have sold us out."

But Scargill said, "I can only come out here and reflect the decision of the conference, which was taken democratically." The conference, he then said, "decided that the National Union of Mineworkers should organize a return to work on Tuesday and that the dispute in the industry will continue until its aims are completely fulfilled, and there is an amnesty for those dismissed in the dispute."

In effect, the delegates have not ruled out local regions fighting against coal pit closures and job losses -- the issues of the strike -- by other means. Scargill warned against underestimating the union's ability to take further action.

Some militant officials have talked about "guerrilla-type warfare" in the pits and work-to-rule slowdown schemes. But coal board officials said that they did not think this would happen and that talks on retroactive wage increases would not begin until the mines were working normally again.

What happened today is that a majority of the regional union leaders overruled Scargill. They decided that the surge back to work by thousands of miners in recent weeks was on the brink of becoming a flood and that the only chance to avoid shattering the union was to go back to work together, without accepting the coal board's plans for the future of the industry. Slightly less than half of the miners were still on strike before today's meeting, according to generally accepted coal board figures.

The back-to-work motion that won approval was put forward by the delegation from South Wales, Britain's third-largest coal-producing region and previously among the most militant in backing the strike.

Coal board spokesman Michael Eaton welcomed the vote but said he would have preferred that it end with an agreement, and he did not welcome Scargill's assertion that the battle would go on by other means. He said he believed most miners "are frankly fed up with being in battle. They would like to return to work and lead a normal life, and I don't think they will welcome the statements of Mr. Scargill."

The government viewed Scargill throughout the strike not only as a trade union leader seeking to save coal pits and communities but also as a Marxist revolutionary aiming to overthrow the Thatcher government and British capitalism.

The strike has produced extraordinary hardships for the miners and their families. The union provides no strike pay, so a year's salary, about $9,000, has been lost, and virtually all families are deeply in debt. The strike was provoked by the coal board's plan to close the 20 of Britain's 174 coal pits that were losing substantial sums of money. The resultant loss of 20,000 jobs would come mostly through retirements, the coal board said.

As the strike evolved, however, the key issue became the board's broader general proposal to close what it considered to be "uneconomic pits." Money-losing pits had been closed during all previous governments as Britain's markets for coal dwindled. But Scargill maintained that pits should close only when they were exhausted of coal or unsafe.

Today's action appears to solidify management's right to make the final decision, although new review procedures have been set up to allow all sides to make their arguments.

The miners are to go back without agreement by the coal board to a major added miner demand: reinstatement of about 700 miners who were fired during the strike for offenses ranging from assault to trying to take a bag of coal to heat their homes. Eaton said there would be no rehiring of those convicted of serious violence or damaging board property. But he suggested that lesser infractions might be set aside.

The strike, which began in most areas on March 12, 1984, has cost at least $1.6 billion, according to the government. But other economists put the figure at about $3 billion, including imported oil and coal, police costs and lost revenues.

Police have estimated that about 1,700 miners and police have been injured, and at least one death is attributed to the strike.

As the hardships built up, the government began enticing miners back to work while at the same time taking a hard line in negotiations. The absence of any hope in recent weeks for a negotiated settlement, in which Scargill accepted the board's right to close uneconomic pits, also accelerated the drift back to work.

But the cost of the strike goes far beyond monetary estimates.

Although there were no power shortages or inconveniences to the vast majority of the British public, the strike dominated a year of politics here. It served as a backdrop to other disputes and a focus of attention on record 13.9 percent unemployment and rich-poor, south-north divisions in this country. It exposed Britons to an almost nightly dose of television violence as pickets and police clashed in scenes that unnerved the population.

The images of the strike, government officials acknowledge, also undoubtedly forestalled new investment from abroad as investors wondered whether the country was reverting to its strike-prone past.

The walkout split miners' families, as fathers went back to work while the more militant sons stayed out. It split one venerable British institution, the miners' union, from another, the police.

At the outset, Scargill made what is widely viewed to have been a crucial mistake. He called the strike without calling a national vote by miners. About a fourth of them, including 45,000 in Nottinghamshire, refused to walk out without a vote. In part because Scargill could not unify his own union, virtually no other union gave him support. The violence on the picket lines also was disavowed by other unions.

Scargill said today that "the trade union movement, with a few notable exceptions, has left this union isolated." Some observers say the union movement generally has been weakened. Others note that more moderate mine leaders have emerged who say they want to restore democracy to the union.

The strike also took a toll on Britain's opposition Labor Party, normally the voice of the working class. The strike tactics and Scargill's rhetoric made it difficult for Labor leader Neil Kinnock to lend any clear support.

Many observers say that attention now will turn to other issues, which could spell trouble for Thatcher, who has not reduced unemployment and has made little progress on reviving the economy.