The UK Supreme Court has ruled that the PSNI was wrong not to investigate allegations of torture used against the 'Hooded Men' 50 years ago.
It said the 2014 decision had been based on a "seriously flawed" report and ought to be quashed.
A solicitor for the group, Darragh Mackin, said it was a "landmark victory".
"It was always clear that the initial investigation by the PSNI was nothing more than a window dressing exercise which only sought to pay lip service to the term 'investigation'", he said.
The men were a group of 14 individuals selected for extreme interrogation techniques during internment in Northern Ireland in 1971.
They were among 350 people arrested during internment in August 1971.
They were taken to Ballykelly Army Camp in Co Derry where they were subjected to treatment which judges in Northern Ireland have ruled would amount to torture were it to happen today.
It included being hooded, placed in stress positions for long periods, subjected to sustained loud noise and denied food, water and sleep.
We need your consent to load this rte-player contentWe use rte-player to manage extra content that can set cookies on your device and collect data about your activity. Please review their details and accept them to load the content.Manage Preferences
The men also said they were beaten and thrown hooded from helicopters that they believed were flying at height, but were in fact hovering close to the ground.
In 1978, the European Court of Human Rights held that the UK had carried out inhuman and degrading treatment, but fell short of defining it as torture.
In 2014, the Irish government asked the ECHR to revise its judgment following revelations in an RTÉ Investigates documentary, 'The Torture Files', that several British ministers had been made aware of the interrogation plan, and that the severity of the impact of the techniques had been withheld from subsequent legal proceedings.
That request was rejected by the ECHR in 2018 and again later the same year when the decision was appealed by the Irish government.
The case was supported by Amnesty International in Northern Ireland.
The PSNI took the case to the UK's highest court having failed in Belfast's Court of Appeal to overturn a High Court ruling that found the PSNI should revisit its decision to end its investigation into the treatment of the men.
Delivering his judgment, Lord Hodge referred to the RTÉ documentary, which referred to a British government memorandum, known as the "Rees Memo", which "referred to the use of torture and to its approval by UK ministers".
Following the broadcast, the PSNI considered whether there was sufficient evidence to warrant a new investigation, but concluded that there was not.
Lord Hodge said: "There is no evidence that anyone involved in the authorisation or operation of the hooded men's ill-treatment has ever been the subject of criminal charges.
"The court finds that the PSNI's decision taken on 17 October 2014 not to investigate further the allegation in the Rees Memo was based on a seriously flawed report, was therefore irrational, and falls to be quashed."
The PSNI said it welcomed "the clarity [the judgment] brings to some complex legal issues".
Assistant Chief Constable Jonathan Roberts added: "We recognise the difficult realities that victims, families, friends and broader society continue to deal with as a result of our troubled past.
"We will now take time to study today's judgment around these complex legacy issues in detail and we will carefully consider its implications for future legacy investigations.
"If we are to build a safe, confident and peaceful society, then we must find a way of dealing with our past and we are committed to playing our part in that process."
This afternoon, the PSNI issued a second statement on the Supreme Court judgement.
It said it had appealed the case to the highest UK court in order to establish the extent to which its legal obligations under the European Convention on Human Rights, applied to legacy cases.
It said it welcomed the "clear legal ruling" that there was no legal obligation to investigate such cases.
"We will now carefully consider the judgements and their impact on the legacy caseload."
One of the issues under consideration at the Supreme Court was the suitability of the PSNI to carry out legacy investigations.
The judges found that there was nothing to suggest that the PSNI's legacy wing could not assign officers to carry out a fresh investigation in the Hooded Men case or other legacy cases, to the proper standard.
The Taoiseach has described the ruling as "a vindication of the campaign of the hooded men".
Speaking in Brussels today, Micheál Martin said: "There should have been an investigation much, much earlier in what was clear use of torture and an abuse of the basic human rights of those people.
"Internment itself was wrong, should never have happened at a time, and did an awful lot of damage to individuals and to society in Northern Ireland."
Minister for Foreign Affairs Simon Coveney said: "This is an important and welcome verdict for the men and their families who have campaigned tirelessly. My department is studying the detail of the verdict closely and will remain in contact with them."
Sinn Féin justice spokesperson Martin Kenny said: "These men have campaigned for almost 50 years for truth and justice. It is a campaign that I and my colleagues have always supported and will continue to support.
"It is clear from this verdict that any new investigation must also be entirely independent of the PSNI and other members of the British policing and security forces."
The case has been one of Northern Ireland's most controversial and long-running legal wrangles.
Meanwhile, one of the men, Francis McGuigan, told RTÉ News he still suffers with the trauma of what he experienced following internment in 1971.
"I still have nightmares, I still get afraid to go to bed at night because I am having a bad day."