Almost two decades passed between the killing of Stephen Lawrence on 22 April 1993 and the conviction of Gary Dobson and David Norris on 3 January 2012. That those years were also marked by profound changes in British society, in police practice and in judicial procedure is a measure of the significance that this one case came to acquire. The Stephen Lawrence of 1993 was a promising 18-year-old A-level pupil and a much-loved son, who was set upon at a bus stop in south-east London. The Stephen Lawrence of 2012 remains all that, but also an emblem for much of what was – and to an extent still is – wrong with Britain.

It would be tempting to conclude that now justice has been done, the Lawrence family can remember their son in peace and the country can put the whole sickening business behind it. But justice is not complete, and even if it were, the one does not – and should not – presuppose the other.

Yes, in many respects, justice has been done. Two men, both teenagers at the time, have been convicted of Stephen Lawrence's racist murder on the basis of forensic evidence obtained through techniques developed only recently. That the jury was unanimous and returned its verdict so relatively quickly offers welcome certainty after so many years of false starts and hesitation.

As Neville Lawrence noted yesterday, however, the conviction of two men does not mean that all his son's killers have been brought to justice. Five were arrested initially, with two charged before the case was dropped. Three were tried, and acquitted, after a private prosecution brought by the family in 1996. The police believe as many as 11 people could have taken part. The truth is that one or more of the killers have still eluded the law. Nor, given the highly technical nature of the crucial evidence, can an appeal be excluded. Even now, this case may not be over.

And, quite beyond the strictly judicial elements, there are good reasons why it should not be consigned so readily to history. The shooting of an Indian student on Boxing Day, in a crime Manchester police are treating as perhaps racially motivated, is only the latest sign that racial difference is, for a very few sick souls, a reason to end a life.

While a crime of the most heinous variety, however, and one still not fully punished, the killing of Stephen Lawrence has left a salutary, even a positive legacy on aspects of British life. As Brian Cathcart argues on the opposite page, the murder brought home to many white Britons for the first time, the reality of racial hatred. The inquiry by Sir William Macpherson into the failure of the Metropolitan Police investigation, which reported in 1999, exposed the persistence of racism in the police – institutionalised racism, as he termed it – almost a generation after Lord Scarman had identified racial discrimination by police as a contributory cause of the Brixton riots.

Among the results were changes to police practice that required racial aspects of any case to be recorded, as well as the creation of new advisory and liaison groups. Another was an end to the 800-year-old principle of double jeopardy, which meant that someone who had been acquitted could not stand trial for the same crime again. Without that, Dobson would not have been tried, still less convicted, this time.

A further consequence might be the far greater recognition that exists today of the real menace represented not just by racist violence, but by racist attitudes in general. If the 18 years since the murder of Stephen Lawrence have changed anything, it is the broad acceptance at all levels of society that racism can never be condoned.

Which is also where it becomes clear how much remains to be done in the matter of race and prejudice in Britain. There are still parts of many cities, but particularly London, which remain essentially segregated by race, and where racist attitudes are rife. Police culture may have changed, but this has not reached every officer. Nor, as the aftermath of the shooting of Mark Duggan in Tottenham last August illustrated, are the police always as socially sensitive as they should be.

And while changed attitudes and improved technology made the trial of Dobson and Norris possible, it is probably fair to say that neither the trial, nor yesterday's conviction, would have been achieved without the persistence and determination of Doreen Lawrence. This is to her enormous credit. But justice for a murdered teenager, whatever his ethnicity, should be fundamental to the system. It should not have to depend on the devotion of a mother.

* Stephen Lawrence: How the case breakthrough came
* A shrunken family: The first journalist to interview the Lawrences recalls the scene
* The science that helped convict Gary Dobson