The Met Police failed to warn people they were the victims of phone hacking by the News of the World, a judicial review has ruled.
The Met Commissioner accepted that the failure to warn victims was unlawful.
Ex-Deputy PM Lord Prescott, Labour MP Chris Bryant, ex-Scotland Yard deputy assistant commissioner Brian Paddick and two others had pushed for a review.
The men, some of whom received payouts from the newspaper's owner, argued their human rights had been breached.
Outside the Royal Courts of Justice in London, Lord Prescott said he would not be seeking damages from the police.
"I just wanted them to admit they weren't doing their job properly. In this country we expect police to get on with their job impartially, and they didn't in this case."
He was among dozens of people who received settlements from News International after the extent of hacking was revealed.
He received £40,000, and Mr Bryant was awarded £30,000.
The case concerned the lawfulness of the original 2006 police investigation into phone hacking, and the failure to notify victims.
Lord Prescott said: "It's taken me 19 months to finally get justice. Time and again I was told by the Metropolitan Police that I had not been targeted by Rupert Murdoch's News of the World. But I refused to accept this was the case.
"Thanks to this judicial review, the Metropolitan Police has finally apologised for its failure to properly investigate, and inform victims, of the criminal acts of phone hacking committed by the News of the World."
He said it remained "a big question" as to why the police did not notify the victims.
He said he was told several times by police that "there was nothing there," and eventually it was revealed there were 44 instances of hacking of his phone.
The other two applicants in the case were Ben Jackson, the former assistant to the actor Jude Law, and an applicant known only as HJK.
The Metropolitan Police said it "accepts more should have been done by police in relation to those identified as victims and potential victims of phone hacking several years ago."
"How the MPS treats victims goes to the very heart of what we do. It was important that this case did not result in such a wide duty being placed on police officers that it could direct them away from their core purpose of preventing and detecting crime."
All the claimants were receiving personal apologies from the Metropolitan Police Service, but "today's settlement does not entail damages being paid by the MPS and, as the court has made clear, sets no precedent for the future," the Met said.
BBC legal correspondent Clive Coleman said Tuesday's order represents a defeat for the Metropolitan police, and an admission that there were flaws in the initial 2006 investigation in failing to notify potential victims of phone hacking.
The Met Police are re-examining the entire case dating back to 2006, when the News of the World's former royal editor, Clive Goodman, and private investigator Glenn Mulcaire were jailed for hacking into the mobile phone voicemails of royal aides.
Since then, a series of inquiries and legal cases have been exploring just how widespread the practice was, and the newspaper was shut by its owner News International.
Operation Weeting is looking at allegations of hacking by News of the World into private voicemails.
Mr Bryant said it was "still a complete mystery to me why the police failed properly to investigate the News of the World in 2006, why they failed to examine the material they had garnered from Mr Mulcaire, why they continued to tell parliament that they had contacted all the victims when they hadn't, why they refused to show me the material that related to me and why they refused to reopen the investigation even when there was clear evidence that the original investigation had only scratched the surface of the criminality at News International."
The ruling comes a day after police confirmed that they believed 829 people were "likely" victims of phone-hacking by newspapers.
Appearing at the Leveson Inquiry into the culture, practice and ethics of the press, Deputy Assistant Commissioner Sue Akers said 581 of those people had been contacted.
However, 231 could not be identified, and 17 had not been told due to "operational reasons".