Instead, Ms Mapp alleges, Metropolitan Police officers assaulted her and her two sons, aged 10 and 12, and arrested her sister, Jacintha, for breach of the peace.
The two men, meanwhile, stood and watched. Police, she said, ignored bystanders who pointed them out.
"I keep asking myself how they could have got it so wrong," said Ms Mapp, 40, a college lecturer, who has described the incident in a submission to the Stephen Lawrence inquiry.
"We were two women and three children. Why did they assume we were the criminals?"
The explanation, she believes, is depressingly simple. They were black; everyone else at the scene was white. When police arrived, her 12-year- old son was agitated and upset. Despite his age and size - 4ft 7in tall - officers saw a young black male and, his mother claims, acted according to the well-worn stereotype.
Ms Mapp's story illustrates the daunting task facing Sir William Macpherson of Cluny, chairman of the Lawrence inquiry, as he and his advisers seek to identify the lessons to be learnt from the police investigation of Stephen's murder.
It has disturbing echoes of a case in Cardiff last year in which two black students were arrested after flagging down a police car while they were being attacked by a racist gang. Officers sprayed one of the students with CS gas.
Charges were eventually dropped because the episode had been filmed by closed- circuit cameras.
Ms Mapp was driving Jacintha and her 12-year-old daughter home on a Sunday evening after they and her sons had all spent the day together, eating lunch and watching a cricket match on television.
On the way, they stopped outside a mini-market, where the confrontation with the two men took place. They kicked Ms Mapp's car, shouted racist obscenities at her and her elder son, and threatened to "blade" them both, she alleges. She went into the shop and called police and a few minutes later, nine officers arrived in a van. "They got out and went straight for my 12-year-old," she said.
"Two of them grabbed him under the arms and slammed him against the shutters of the shop. I had an overwhelming feeling of panic. Everything seemed to be happening in slow motion. I ran over and pointed at the white men, explaining that they had attacked us. Two policemen got hold of me and pinned me against the wall. My other boy, the 10-year-old, tugged at the arm of one of the officers, telling him to let me go. The officer elbowed him in the forehead and knocked him to the ground.
"The police were threatening to arrest the elder boy. He was hysterical, and my sister tried to pull him away from them.
"They grabbed her by the hair and swung her around. Then I saw them putting handcuffs on her."
At the local station, where Jacintha was released without charge, Ms Mapp had the boys' injuries - cuts and bruises - recorded by a police doctor. They were also examined by the family's GP.
Determined to take action against the officers, she contacted the area police complaints unit and enlisted the support of her MP and local council leader.
But before she could make a statement, the police arrested one of her two alleged assailants on the basis of the information that she had given them. She was told that her complaint could not be investigated until the man had stood trial because there was a risk of prejudicing his case - an argument rejected by her solicitor, Clifford Tibber, who says that the two incidents are completely separate.
As time passes, the prospect of redress appears to become increasingly remote. Moreover, the six-month deadline for a criminal prosecution to be brought against the police officers in a magistrates' court is about to expire.
Ms Mapp is horrified that the officers continue to serve in one of the most racially mixed areas of London.
Her sons, who had never experienced racism before, are scarred by the experience. "They were in a terrible state for weeks," she said.
"When we went to the Notting Hill Carnival recently, they were really nervous to see all the policemen there."
Sitting in her kitchen, flicking through a bulging file about the case, Ms Mapp said: "I am totally shattered. I just can't believe that something like this can happen here in 1998."
Scotland Yard said last weekend: "Internal investigations take second place to criminal or civil proceedings. Once a criminal trial is over, the complaint will go ahead."