It was a momentous occasion. Unlike those carefully choreographed events at Stormont or Hillsborough Castle marked as "historic days" for the peace process, the scenes of spontaneous joy and raw emotion on the streets of Derry after the Saville report were truly moving.

Telling the truth about the Bloody Sunday dead did more for the peace process than a thousand stage-managed political handshakes or press conferences in salubrious surroundings. The murder of 14 unarmed civil rights marchers has been a cancer poisoning the nationalist community's relationship with Britain for nearly four decades.

The victorious thumbs-up signs from relatives through the lattice windows of Derry's Guildhall was the first indication that healing, slow as it will be, is now possible.

The victims – shot as they crawled away from soldiers, as they lay already wounded on the ground, as they waved white handkerchiefs – were all unequivocally declared innocent, and the soldiers exposed as liars.

"Does it need recourse to law/To tell ten thousand what they saw" Thomas Kinsella's powerful poem, 'The Butcher's Dozen', about Bloody Sunday, declares. The people of Derry didn't need to be told the truth – they witnessed it with their own eyes – but they needed the truth to be told by Britain to the world.

It must be remembered that the Bloody Sunday campaign for justice didn't always have the extensive support it won in recent years. That justice is secured, however belatedly, is due to the tenacity of the families and of Eamonn McCann, one of the civil rights leaders present in the Bogside that day, who has never given up.

The dignity of David Cameron's unambiguous apology resulted in a scene few would have anticipated – a Tory Prime Minister clapped and cheered by nationalist Derry.

By contrast, the graceless response of DUP MP Gregory Campbell shows the bitter psyche some unionists still possess. "People will be glad this sorry saga of a report is finally over and done with," he pronounced.

Unionists reiterate the £200m cost of Saville and the fact that republicans committed atrocities. The lives of those killed at La Mon, Kingsmill, Omagh, and by the Shankill bomb count every bit as much as those of Bloody Sunday.

But what unionists stubbornly refuse to accept is that no-one is under any illusions about the nature of paramilitary organisations.

The state, by contrast, claims to operate according to democracy and the rule of law. So when it shoots dead 14 of its own citizens in public, an inquiry is essential.

And had the state admitted the innocence of the dead – rather than criminalising them in the Widgery report – and had soldiers not persistently lied to Saville – the length and expense of the inquiry would have been greatly reduced.

Some of the Bloody Sunday families understandably want soldiers prosecuted. But convictions seem unlikely. The standard of proof required in the criminal courts is higher than that in Saville. What is achievable is that those soldiers who lied to the inquiry be prosecuted for perjury.

While much of Saville is to be welcomed, parts are seriously inadequate. There is a danger that the Paratroopers on the ground that day and Lt Col Derek Wilford, their commanding officer, will alone become the fall guys.

The chain of guilt goes far higher. General Sir Mike Jackson, who went on to hold the top post in the British Army, was involved in writing the military's original account of Bloody Sunday.

It was the British Home Secretary, Reginald Maudling, who lied to the House of Commons and said the paratroopers had acted in self-defence. It was Prime Minister Edward Heath who appointed Widgery to pen his whitewash report with the warning: "Don't forget we're fighting a propaganda war."

The British authorities disseminated black propaganda about the dead and many media outlets – either too lazy or slavish – enthusiastically repeated the lies.

It was the queen, on government advice, who decorated the now scapegoated Wilford shortly after Bloody Sunday. The endorsement of the Bloody Sunday massacre, and the cover-up, goes right to the top. It would have been healthier to acknowledge this.

Saville says soldiers on the ground lost control. But why would any right-thinking military chiefs station the paratroopers in Derry anyway?

The regiment's brutal reputation was well known. Nine days before Bloody Sunday, it fired rubber bullets and CS gas at close range at civil rights marchers on a beach just outside Derry. John Hume witnessed soldiers beat demonstrators to a pulp.

Five months before Bloody Sunday, the Paras killed 11 people – 10 men, including a priest, and a mother of eight – in West Belfast. Having such a regiment anywhere near Derry on 30 January 1972 was criminally reckless.

Yet some truth is better than none at all. The North remains a place of secrets and shadows. Gerry Adams still won't admit he was in the IRA and the Provisionals continue to lie about their own dark deeds. Sinn Féin and the IRA must step up to the mark on transparency just as much as the British did.

But no-one can deny that the North has changed. On Bloody Sunday, they marched for jobs, houses, votes and equality. Religious discrimination has largely ended. The North is no longer an Orange state. The lives of those celebrating the Saville report in Guildhall Square last week are markedly better than those of the civil rights protestors they gathered to honour. For that we must all rejoice.