By last Friday afternoon the rumor has swept up every alleyway: skinheads, the militant right-wing cult group, were planning a march through the center of Handsworth, Birmingham's main minority neighborhood.

The local police superintendent, David Webb, who is credited with developing England's model police-community-relations programs here, took to the streets to reassure an aroused community that no such march could occur. All the same, hundreds of people lined up expectantly ang angrily along Soho Road. It was a hot, muggy night, and trouble was in the air.

A few minutes before 10 p.m., someone on a citizens' band radio channel declared falsely that Handsworth was rioting. Moments later a brick flew at Webb, who in plain-clothes was the sole policeman on the street with the crowd. A night of looting and rioting followed.

Birmingham, England's second-largest city, was the last of the major metropolitan areas to be struck by the street violence that rippled across the country last week. That this city's impoverished area, once considered potentially the most explosive in the country, remained nonviolent as long as it did relfects at least in part the relative success of an earnest community-relations program.

Now an uneasy calm has returned, allowing time for assessment of the cause of the disturbances. But the picture is complicated, and explanation of what happened vary.

Each area in which there was trouble has its own historical traditions, and each group in the multiracial mix of blacks, Asians and whites who were involved carry their own grudges. In general, the riots appear to have merged the feelings of economic deprivation and the pain of racism with animosity toward the police and a sense of letting go.

Lord Scarman, who is charged with investigating commmunity relations in Britain's restless cities, arrived in Birmingham today and told reporters he did not think the violence in places outside London had much to do with racial factors. Instead, he blamed the flare-ups on a "copycat syndrome" among youths and on a run of hot summer nights.

As the rioting spread, British officials have shown a tendency to speak less about the tension and despair underlying England's inner-city neighborhoods and to lash out instead at criminal or political elements believed to have ignited the simmering social tensions.

Birmingham's Lord Mayor Ken Barton blames extremists on both left and right for fomenting the unrest here.

But if there were provocations, they clearly fell on receptive ground. Birmingham's Handsworth area, a multiracial community that long ago sank to society's nadir, does at least lack the poisoned relationship between its police and public that London's Brixton or liverpool's Toxteth suffer, yet it erupted nonetheless. Some who live here and thought they knew their neighborhood saw things that continue to stun them.

James Hunte, a community leader, talks of how he looked on in wonder as a 9-year-old boy led a well-ordered march of blacks and whites fiercely chanting "skinheads, skinheads," through Handsworth. The scene, Hunte says, sent a chill through him.

A sense of fear still fills some in this industrial city in central England. David Shaw, 29-year-old reporter for the Birmingham Evening News, says he does not want his daughter and wife to shop in the center city, where last Saturday afternoon a band of young rioters ran rampant.

Of the roughly 200 rioters arrested here, most were remanded into custody during quick hearings this week that were notable for an evident court intention to consider bail only in a few cases. Still, with another 16,000 young people due to graduate from school in less than two weeks, who will spill into a job market whose unemployment rate has nearly doubled to 12 percent in one year, the prospects for further unrest seem to multiply.

Before last weekend's rioting, Birmingham had gone four years since its last uprising. Since then the city has pioneered in its community relations efforts, taking police out of patrolling cars and putting them back on foot patrol to encourage closer contact with the public -- in general, reviving the old bobby-on-the-beat concept.

But the program could not be expected to address the basic causes of the dissatisfication in the community, which are rooted in economic and social aspects of the British system, nor could this type of policing really do much to reform some of the core criminal groups in the area.

"You could say some of us have come to the conclusion that the only way to survive is by organized vandalism," said 22-year-old unemployed construction worker and Handsworth resident, who, like most other youths interviewed, preferred not to give his last name. "This is a racist system altogether, from local government to the immigration system."

the dissatisfaction has deepened as a result of Britian's recession, which in some cases has put the parents of jobless youths out of work as well.

A determination of the government of Prime Minister Margaret Thatcher to follow through on a tough program of budget cuts has been taken as an indication of government's uncaring or insensitive attitude to the pain of those put or kept out of work and running out of hope. "This government is hard and it has made people hard," said Edward, a 19-year-old originally from the island of Barbados. "The government is unbending and we have shown we are also unbending."

In the destruction and additonal distress brought on by the riot here, there are still faint signs of a new order, or at least organization, being established within the multiracial swirl. The merchants along Soho Road, most of whom are Indians and Pakistanis, met last night for the first time to talk over the situation. They have agreed to form a merchant's association for their mutual protection and other interests.

For the moment, Police Superintendent Webb, The 26-year police veteran who briefly entertained the thought of resigning over the rioting, actually sees cause for relief. "We got off tremendously easy," he said. "Although store windows were smashed, we didn't get a single shop burned down. Most importantly, it hasn't seriously damaged police relations with the community.