Among them is a young man who ought to feel safe anywhere. Audley Harrison - captain of the England boxing team at last month's Commonwealth Games, and a gold medallist in the super- heavyweight division - is a boxer of awesome punching power, who has promised to land a world title when he turns professional.
He stands 6ft 6in and weighs 18 stone, but that didn't seem to bother the police officers who he said set about him at Stoke Newington police station, north London, when he went with his former girlfriend to give a statement about a violent arrest that they had witnessed.
Hazel Bruno-Gilbert, an accounts manager, said she was accosted by half a dozen officers before being herself charged with assault. Mr Harrison, who almost passed out after being gripped in a neck-hold, was charged with obstructing a police officer. The charges were thrown out by magistrates, despite nine police officers giving evidence against the couple. In January, the pair accepted pounds 62,500 in compensation.
Recalling the episode yesterday, Mr Harrison, 27, said: "One had me by the neck and two others were holding my arms. I could not breathe. I thought I was going to lose my life in there. They dragged me to the back of the station and stood on my face."
None of the officers was disciplined, although one was later jailed for assault after using a dangerous neck-hold in a separate incident.
Mr Harrison said Sir Paul's apology to the Lawrence family yesterday meant nothing unless officers were punished for their wrongdoing. "If he wants the black community to have any faith in the police then officers must be accountable."
Daniel Goswell is another black man with a grievance against the police. He was truncheoned over the head while wearing handcuffs after being arrested as he sat in his car waiting for his girlfriend.
Mr Goswell, from Woolwich, south London, was awarded pounds 302,000 in damages in 1996, later reduced to pounds 50,000 after an appeal. Sir Paul personally looked into the case and sacked the officer concerned, although he was later reinstated by Michael Howard, Home Secretary at the time.
Mr Goswell's solicitor, Jane Deighton, said yesterday that criminal charges should have been brought. "If a black man had done the same thing to a police officer he would go to prison for five years," she said.
Two other men, Wayne Taylor and Leroy McDowell - both of whom suffer from sickle cell anaemia - were stopped by police as they returned in a new car from a London nightclub. Officers searched them, saying they were "in a drugs-related area". When they protested, both men were subjected to racial abuse and arrested. They were refused medical attention when their conditions deteriorated in the police cells. The Metropolitan Police agreed to pay them pounds 38,000 in compensation last November.
Mr McDowell, 34, said last night: "Sir Paul is quick to label black people as muggers but he won't take criticism of his own force or accept responsibility. Racism in the police is blatant and everybody knows it."
In another incident, Emmanuel Afriye, a Ghanaian student, was awarded pounds 6,000 in damages last year after a court decided police had stopped his car simply because of his colour. The jury refused to accept evidence from a succession of officers that Mr Afriye, who was questioned about his immigration status, was stopped because of bad driving.
People from other ethnic minorities have also been victims of brutality. Kenneth Shu, a Chinese hairdresser, won pounds 220,000 damages in 1996 after a jury accepted that he had been attacked by police after he refused to let them into his London home without a warrant.
Louise Christian, a civil rights lawyer, said there was "clearly institutionalised racism" in the Metropolitan Police. She said: "Not only does it affect black people who are unlawfully arrested and maliciously prosecuted it also results in victims of crime being arrested themselves or not taken seriously."
Evidence shows that black people are up to eight times more likely to be stopped and searched by the police as whites, and this is thought to be a major factor in the alienation of black youth from the rest of society. Four out of five young blacks told a University of Warwick study published in August that they expected British race relations to deteriorate.