For Doreen and Neville Lawrence, the mark left by the loss of their eldest son has been indelible. The world has its own picture of Stephen Lawrence. It sits alongside the detached iconic images we carry of others we never really knew: Martin Luther King, Malcolm X, Che Guevara.

But Stephen wasn’t a poster, a banner or a T-shirt; he was their son. His brutal killing in 1993, at the hands of white racist thugs on a cold, dark night in south-east London, affected and ultimately changed a nation, but it lives with the Lawrences in a way that only they can understand.

Perhaps the only institution from which the shadow has never moved has been the Metropolitan police. But on Wednesday, after multiple investigations, multiple failures, limited success and decades of the harshest scrutiny, it moved to do something about that by formally declaring that the inquiry and their hopes of bringing all of the notorious racist attackers to justice “is unlikely to progress further”.

This no doubt speaks to the fact that the trail is cold and resources are finite. But it also feels like something else, the drawing of a line under a case that has defined policing in Britain for a generation. That’s an understandable if regrettable move by the Met. There is a generation now that has only the haziest recall of the Stephen Lawrence murder, and may not have heard of it at all were it not a staple of how schools observe Black History Month.

Some of those for whom the case is no more than a curio are youthful police officers. It would not be surprising if – with no prospect of a breakthrough – the force now wants them to get on with their job without the psychological millstone of its biggest failure. Amid speculation about the Met’s new position, Doreen Lawrence herself has urged them to “be honest”. Still, the Met, and police officers everywhere, should tread carefully. Whether the inquiry is shelved, or reawakened by a lead from the BBC documentary on the case, which airs next week (as the Met now hopes), this is not a case that any progressive police officer should dump in the archive, or should be allowed to.

From the Stephen Lawrence case, and most notably the public inquiry it engendered, Britain learned what happens when police officers see themselves not as public servants deployed to protect communities, but as an unrepresentative force apart, acting without compassion or empathy. Britain learned of the uncomfortable nexus between criminals and police at a time when the force should have been securing justice for a black teenager, his family and Duwayne Brooks, the traumatised friend who saw him struck down.

Doreen Lawrence with leading lawyer Imran Khan, who has claimed institutional racism is ‘thriving’ in the Met. Photograph: Nick Ansell/PA

Quite apart from what emerged about attitudes in Britain in the 1990s, we learned much of the sheer incompetence of our policing at that time. The leads phoned in by witnesses that might have led to early arrests, but didn’t. The failure to deal with Brooks and the Lawrences in ways that might have assisted a meaningful investigation. The bungling of forensics. The piteous standard of interrogation that allowed the suspects to confound the investigation in its early incarnation. One senior officer brought in to review and address the inadequacies told me that what shocked him was not the obvious bias, but the glaring lack of craft. It wasn’t just that the force seemed ill-equipped to tackle racist crime. It was deficient in its ability to tackle serious crime of any motivation.

The legacy of the Lawrences has not just been to make a police force better at dealing with race offences. It has, by shining a light on poor police practice, made us all safer. Enhanced police practice in the field of forensics led to the conviction in 2012, 19 years after Stephen’s murder, of two of his attackers, David Norris and Gary Dobson.

For a while at least, it ceased to be the burden on minority Britons to prove that there was unfairness and racism

And the case made a country think. About whether its inequalities could really mean that a young man rushing home could be stabbed to death in the street without society exacting a price. It led the Daily Mail, acting famously against type then and since, to champion the cause of a black Briton. There was also, at the instigation of Sir William Macpherson’s inquiry, a discussion about institutions and the biases that led them, and still lead them, to disadvantage minority Britons.

The process did something else that was crucial. For a while at least, it ceased to be the burden on minority Britons to prove that there was unfairness and racism. The case, diagnosed and dissected in public, proved it. It was possible to argue about the scale of those injustices, but not that they were happening. They were relayed to the world.

In the intervening years, we have seen the reactionary pushback, with models of responsive, connected policing that emerged from the process dismissed as politically correct, a steady baleful distancing of the police from communities again, and a concerted rubbishing of the very concept of institutional racism. There is a rearguard, in the media, in academia, that would deny to minorities in this new century their experience of racism itself.

It is against this backdrop that one should consider the Met’s decision to state its new position on the case. It is explicable in itself. Perhaps with the passage of time, it was inevitable. It is undeniably a moment. But what it must not be is a precursor to a wiping or even a whittling away of historical memory. The campaigning and eventually the furore over Stephen’s death made Britain a better country. His life cut short mattered then, it matters now. Those were gains worth fighting to protect.

• Hugh Muir is an associate editor of Guardian Opinion