The Met Police has lost an appeal at the Supreme Court against two victims of black cab rapist John Worboys who won compensation for its failings.
The women were raped by Worboys in 2003 and 2007 and said their treatment by police, who failed to believe their reports, caused them mental harm.
The ruling means police may face human rights actions whenever they fail to properly investigate serious cases.
Human rights organisation Liberty said it was a “landmark” ruling.
The Metropolitan Police said it fully accepts the decision and “there is no doubt that it will have implications” for future investigations.
One of the victims, known as DSD, who was the first of Worboys’ victims to make a complaint to the police in 2003, said: “It has been an emotional day. Fifteen years.”
Referring to the police, she added: “Had you done your job properly, there wouldn’t be 105 victims, there would be one.
“I can take the one. I can’t take the 105.”
Her lawyer Harriet Wistrich said: “It’s a very, very important judgment – very important for vindicating the rights of my two clients but also for the other victims of Worboys.”
The women are also separately pursuing a judicial review of the Parole Board’s decision to release Worboys.
Worboys was able to continue to attack women until he was convicted of 19 offences in 2009, when he was ordered to serve at least eight years in jail.
The Met believe he may have carried out more than 100 rapes and sexual assaults on women in London between 2002 and 2008.
Analysis: Legal correspondent Clive Coleman
The ruling is highly significant for both victims of serious violent crime and for the police forces that investigate it.
It means that if a police force conducts an investigation into the crime which fails in a way which is deemed sufficiently serious, it will be liable to a human rights action brought by the victim.
Successful claims will result in compensation to the victims. The ruling means that there is an additional rigour placed on police forces to ensure they properly investigate violent crime.
The 2010 report by the Independent Police Complaints Commission disclosed many serious failings in the police investigation in Worboys.
So the ruling is likely to lead to more claims by his victims.
However there will be many other victims of violent crime who feel that they were let down by serious police failings, who will now want to consider bringing claims for breach of their human rights.
The women brought their claims under article three of the Human Rights Act – the right not to be subjected to torture or to inhuman or degrading treatment.
Until then, police could not be found to be negligent for generally failing to identify and apprehend an unknown suspect.
The police appealed, arguing that its duty was fulfilled simply by having practices and procedures to investigate in place, although it was agreed that the damages awarded to the women would not be recouped if the appeal succeeded.
Victims let down ‘horrifically’
The Met Police said it “unreservedly apologises to the victims we failed”.
Sir Craig Mackey, deputy commissioner of the Met Police, said in a statement that it had appealed because “police forces needed absolute clarity on the boundaries of police responsibility and liability for their investigations”.
He added: “There is no doubt that it will have implications for how we resource and prioritise our investigations.”
The appeal followed a 2013 High Court ruling which found the Met was liable to the women – known as DSD and NBV – for failures in its investigation.
DSD said she suffered a depressive disorder as a result of her treatment by officers during the 2003 investigation and was awarded £22,250.
NBV claimed she suffered serious distress, anxiety, guilt and an exacerbation of post-traumatic disorder and depression because of her treatment by police. She was awarded £19,000.
Martha Spurrier, director of Liberty, said: “Having already let these women down in the most horrific way, the Met could have accepted the High Court’s ruling four years ago.
“Instead, they used taxpayers’ money to drag them all the way to the highest court in the land.”
The case comes a month after the government announced it would not challenge the Parole Board’s decision to release Worboys after he had served less than 10 years in prison.