A wave of shame spread over Britain today, and Prime Minister Margaret Thatcher described the nation as "worse than numb" following riots at the European Champions' Cup soccer final in Brussels last night that left 38 persons dead and hundreds injured.

Thatcher said she was one of millions here who watched the pregame violence, broadcast live throughout much of Europe, and who saw British supporters of the FC Liverpool soccer club attack panic-stricken fans of Juventus, the opposing team from Turin, Italy. Most of the dead were trampled or crushed when a retaining wall collapsed.

After an emergency meeting this morning with government ministers, Thatcher said that she had authorized an "immediate, initial contribution" of more than $300,000 to the victims and their families among the Italian fans. She indicated that the government would seek legislation regulating the British soccer leagues.

Last night's incident, Thatcher said, is "a very serious blow" to Britain's international standing. It marks the culmination of a years-long pattern of escalating violence at matches here and abroad that has taken an increasing toll in injuries and property damage and gained British fans a reputation as thugs throughout Europe.

Some of the returning Liverpool fans today criticized Belgian police riot control, and a few members of Parliament said that Britons were being condemned for the "accidental" collapse of the wall.

But the overwhelming reaction was one of shame and sorrow -- and guilt for not addressing a national problem that has been long apparent. There was a feeling that Britain's image in the world had been tarnished. Most seemed to agree with Thatcher, who said "those responsible have brought shame and disgrace to their country and to football."

Thatcher sent a personal message to Belgian Prime Minister Wilfried Martens. Queen Elizabeth sent messages to Italian President Sandro Pertini, and King Baudouin of Belgium, expressing her "heartfelt sympathy" over the "shocking events" in Brussels.

In seeking to place blame on the few hundred deemed responsible among the thousands of Liverpool fans who traveled to Brussels, there were charges from the left -- backed by sociologists who have studied soccer violence here -- that the violence is at least in part the result of life in the inner cities where most of Britain's soccer stadiums are located, and the bleak economic conditions of most of the blue-collar crowds that attend.

From the political right, including Thatcher, there were calls for tougher penalties against those convicted of violence at soccer matches.

At the same time, pressure grew from political leaders, distraught soccer fans and even some team managers, for the national Football Association to withdraw English teams voluntarily from all European play during the 1985-86 season, which begins in September. Many commentators said that step would preclude what they felt was the near certain suspension of England by the European Football Union. It is not clear whether such a suspension would extend to teams from Scotland, Wales and Northern Ireland, each of which is governed by an independent Football Association.

"I have to say that I would like to see our authorities . . . after a tragedy like this, where so many people have died, I would like them to say, 'We will withdraw,' " said Barry Davis, the BBC soccer commentator who covered the match from Brussels. "We have to say, 'Enough is enough.' We've got to sort out our own problems before we take them abroad. There were 18 television stations watching that last night. What kind of image can they have gotten?"

The general outcry appeared to reflect both shock and disgust at the Brussels violence. But comments across a wide spectrum of British society today indicated a deeper concern that something has gone seriously wrong in a society in which such tragedies can result over something that is "only a game."

"We have become a sick nation, with a sick disease," said Birmingham City soccer team manager Ron Saunders. "We have no respect for authority . . . . We're becoming a nation of cowards and cheats and bullies."

"Football hooliganism" is a general term for soccer violence here that was only last year considered by a government commission for statutory distinction as a new category of crime. It is not unique to Britain. Soccer matches in Latin America, the Far East and among other European countries have been scenes of the phenomenon.

But Britain always has been different, in its passion for the game that it claims to have invented and in the extent to which fans from communities across the country identify with their teams. Today, soccer games in Britain are considered so violence-prone that this once family-oriented spectator sport largely has been abandoned to the hooligans.

There are a wide variety of explanations offered here for the turn to violence. Sociologist Peter Marsh, a recognized expert on the subject, says it starts as something he identified in a 1978 book as "aggro," a term first used in the 1960s to refer to the behavior of juveniles known as "Teddy-boys," and "Skinheads." As Marsh describes it, "aggro," from "aggravation," is a form of male-bonding behavior that is basically nonviolent.

John Williams, a Leicester University sociologist who last year published a book called "Hooligans Abroad," said today that the problem couldn't be solved by law enforcement.

"It's much more difficult getting to the roots of why some people who go to football matches want to fight other supporters," Williams said.

British fans seem to travel to matches in other countries more than supporters from continental Europe do. In his book, Williams described the effects of that travel among the lower economic classes as a "perceived release from the home patch . . . along with the ritual degradation of foreign culture and territories and celebration of one's own."

Williams and others also point out that what is particularly new about football hooliganism here is not so much the violence but the attention paid to it by the British media, which consistently refer to enthusiastic soccer fans as "animals" and thus may lead them to behave that way. At the same time, extensive pregame media attention always is paid to scheduled games between teams with notoriously violent fans, such as Millwall and Chelsea, causing supporters to come ready for confrontation in the belief their opponents are doing the same.

Still others charge that the violence is perpetrated by small, organized groups of troublemakers who have no interest in the game itself. Liverpool club chairman John Smith today charged that the violence in Brussels was orchestrated by members of the National Front, a right-wing extremist group in Britain.

In response to the escalating violence, the government last year appointed a special study commission to look at ways of preventing it. The study notes that the possible contribution of social conditions to the problem was "outside the scope" of the report but recommended a number of legal and regulatory changes.

Among them are the issuance of membership cards to supporters of British soccer clubs and installation of computer systems to keep track of known troublemakers. Other proposals include banning alcohol sales in and around stadiums, a policy that has brought some success in stemming violence in Scotland and, again, stiffer penalties for those convicted of causing violence.

Perhaps the saddest commentary on what happened in Brussels was offered by Liverpool team manager Joe Fagan, who had planned to retire after the European Cup match.

Appealing to the fans for calm before the game, which went on as scheduled because officials believed that canceling it would provoke more trouble, Fagan broke down and cried. "I don't know why; I dont know why they do it," Fagan told an interviewer last night. "It's not a football match now. And maybe at the end of the day I'll be thankful to get out of it. What a horrible thing to say, to be in the game all this time, and having to say a thing like that."