Doreen Lawrence says police put her through years of grief and uncertainty as Gary Dobson and David Norris found guilty

The mother of Stephen Lawrence accused the police of putting her through 18 years of grief and uncertainty after witnessing the conviction of two of her son's killers for his racist murder nearly a generation ago.

Outside a grey and rainswept central criminal court in London, to cheers from members of the public and campaigners, Doreen Lawrence said she could not celebrate; all she felt was relief that at last "some sort of justice" had been done, with the jury's unanimous guilty verdicts on Gary Dobson, 36, and David Norris, 35.

"How can I celebrate when I know that this day could have come 18 years ago if the police, who were meant to find my son's killers, had not failed so miserably to do so?"

Alongside her but speaking separately, Stephen's father, Neville, thanked the police and prosecutors and did express joy at the convictions. But he qualified his words, saying that five or six men had been responsible for his son's death on 22 April 1993. "I don't think I will be able to rest until they are all brought to justice," he said.

The high-profile status of the Lawrence killing ? its highlighting of racism, incompetence and an apparent vein of corruption in the Metropolitan police, and the way the aftermath of the murder radically changed the face of policing, the law and politics ? was reflected within minutes of the jury foreman pronouncing the "guilty" verdicts in court 16.

David Cameron issued a statement praising the Lawrence family for fighting "tirelessly" for justice. "Today's verdict cannot ease the pain of losing a son. But, for Doreen and Neville Lawrence, I hope that it brings at least some comfort after their years of struggle," he said.

But while the Lawrences hope to see others brought to justice, seven police investigations costing more than ?30m and the latest groundbreaking work by forensic scientists have failed to unearth any new evidence against the Acourt brothers, Neil and Jamie, and Luke Knight ? the three remaining prime suspects for the killing.

A police source said officers would now visit Dobson and Norris in prison to see if they would end their 18-year pact of silence. "We will work on their anger, and see if we persuade them that while they face long sentences the others are free," said the source.

It took just a few seconds for the jury foreman to pass judgment on the cutting-edge scientific evidence presented by the crown against Dobson and Norris after years of humiliating failures by the Metropolitan police.

One spot of the dead teenager's blood, a few fibres and two microscopic hairs brought Dobson and Norris ? who became suspects within hours of the murder in 1993 ? to justice. They will be sentenced on Wednesday. The blood found on the collar of Dobson's jacket was the smallest spot scientists have ever used in a criminal prosecution.

Dobson ? who becomes one of only six people ever to be tried twice for the same offence ? shook his head vigorously as at 2.55pm the foreman pronounced he was guilty of the murder of Stephen Lawrence. Norris gave no reaction to the same verdict. Mr Justice Treacy had ordered the court to remain quiet. "I recognise that this is a time of emotion for many people in court," he said. "I would ask those people to respect the dignity of the courtroom and the feelings of other people. The verdicts in this case will be received in complete silence."

He choreographed a break in proceedings after the verdicts were announced to prevent uproar in court. But when he sent the defendants down to the cells for the 10-minute adjournment, the emotions he had tried to contain spilled over.

As his mother, Pauline, began sobbing in the public gallery above him, Dobson looked from the dock to the jury. "You have condemned an innocent man," he said as he was led away. "I hope you can all live with it."

Above him, his family were urged to take some air, but Pauline Dobson could be heard sobbing loudly and shouting: "This is so wrong. He didn't kill that man, he is innocent."

Below her the composure of Doreen Lawrence ? which she had maintained throughout the seven-week trial ? began to crack. She cried while her son, Stuart, whispered words of comfort to her.

A few feet away Neville Lawrence was openly weeping. Later as the defendants were led away for the day, Dobson shouted to his family: "Stay strong, I love you, don't worry."

While they replied: "We love you Gal, we will fight to the death."

After years of dashed hopes and police failures the pursuit of the much-criticised Metropolitan police produced the evidence the family had been waiting for in 2007. A full forensic review of all the evidence unearthed a microscopic spot of Lawrence's blood in the collar of the jacket seized from Dobson's house. In addition 16 fibres from Lawrence's clothes were found on the jacket and the evidence bag it was held in.

Norris was linked to the scene by a microscopic hair matching the familial DNA of Lawrence and seven fibres from the dead boy's clothes. The defence counsel argued that the evidence was a result of contamination of the exhibits over 18 years. But the jury took just over eight hours to reject this and pronounce guilty verdicts.

The case was one of the most notorious unsolved murders in Britain. The 18-year fight for justice by Lawrence's parents led to a public inquiry which uncovered blunders by the Metropolitan police, blamed on institutional racism, which allowed his killers to escape justice.

Lawrence, 18, was murdered on 22 April 1993, as he and a friend waited for a bus in Eltham, south-east London.

They were attacked by a group of five to six white youths who shouted: "What, what, nigger?" and then rushed towards them, engulfing him by the weight of their number and stabbing him twice in the upper torso.

He ran 300 yards before collapsing and dying.

The former home secretary Jack Straw, who had ordered the public inquiry into the killing and the Metropolitan police's response to it, praised the Lawrences' campaigning work. "Things have improved dramatically and that is down to the extraordinary courage and determination which Neville and Doreen Lawrence showed in keeping alive the case for justice for their murdered son Stephen and for getting on for 19 years they couldn't get anyone convicted for the murder."