Police in Northern Ireland have accepted "full responsibility" for failures resulting in the collapse of the John Downey prosecution.
Chief constable Matt Baggott apologised to the families of the victims and survivors of the Hyde Park atrocity.
"I wish to apologise to the families of the victims and survivors of the Hyde Park atrocity. I deeply regret these failings, which should not have happened," he said.
"We are currently carrying out a check of these cases to ensure the accuracy of information processed by the PSNI."
The legal wrangle raises questions with the Police Service of Northern Ireland (PSNI) which, the court heard, knew about the UK arrest warrant for John Downey but did nothing to correct the error of 2007.
Northern Ireland Secretary Theresa Villiers has said police in Northern Ireland should reflect on "the serious error" following the collapse of the Downey prosecution.
She said the Government does not support amnesties for people wanted in connection with terrorist offences.
"The PSNI will wish to reflect on lessons learned from this case and the circumstances that led to the serious error which occurred," she said.
Mr Baggott said the PSNI accepts the court's decision and full responsibility for the failures which resulted in this outcome.
He added: "We will be referring this matter to the Police Ombudsman for Northern Ireland."
Mr Downey was part of a scheme for dealing with so-called on-the-runs which was set up by the previous Labour Government.
The current Government reviewed the scheme and decided that any future requests should be referred to the devolved authorities in Northern Ireland, with the Northern Ireland Office dealing only with pending cases for which requests had been received before the general election, Ms Villiers said.
She added: "The Government is looking carefully at the judgment of the court, and we are working with the police to identify whether there are other cases similar to that of Mr Downey. It is right that time is taken to consider the full implications of this judgement."
Ms Villiers said the Government believed in upholding the rule of law.
"That is why both the Coalition parties strongly opposed the legislation introduced by the Labour Government in 2005 which would have introduced what was effectively an amnesty for so-called on-the-runs," she said.
"The Government is also clear that terrorist atrocities such as those committed at Hyde Park and Regent's Park never had any justification.
"Those responsible were unable to see that a path of violence would never succeed, and that the status of Northern Ireland will only ever be determined through democracy and consent.
"It is, though, also important to recognise how far we have come since this despicable act of terrorism over 30 years ago. Only by working together can the community in Northern Ireland achieve a more peaceful, stable and prosperous future."
Ms Villiers said she fully understood the dismay of the victims' families.
"It is of course a matter of sadness and regret that 30 years on still no one has been convicted of the Hyde Park bombing," she told the BBC.
"Certainly I will be speaking to both the Chief Constable and the Northern Ireland Justice Minister David Ford about what further inquiries are needed.
"It is absolutely vital that what went wrong at the PSNI on this matter is properly investigated and independently investigated."
Peter Hain, who was Northern Secretary between 2005 and 2007, said that while he understood the anger of the families, the arrangement for dealing with the on-the-runs had been an essential part of the peace process.
"You often get this at the end of wars and conflicts. You often get what seem to be unseemly processes in order to end the violence and stop them happening again," he told the BBC Radio 4 PM programme.
"Awful atrocities like this hideous attack on London could happen and would still have been happening had there not been put in train - both before Tony Blair became prime minister and then at the Good Friday agreement - a process that ended the horror, the war, the terrorism and brought Northern Ireland to where we are now with old enemies sharing power."
Mr Hain - who said that he was no longer in the post when the letter was sent to Mr Downey assuring him that he was no longer at risk of prosecution - nevertheless said he had been "astonished" by what had happened in this particular case.
"I am surprised about the detail of this case because in other cases, of which there were many, they (the PSNI) had conducted a painstaking investigation to check carefully and methodically whether it was possible to find the evidence to bring a prosecution," he said.
"They decided in Mr Downey's case that there wasn't. He was a suspect for this crime and a suspect alone. It seems that there was an error."