Mr Brown said people were "outraged" by the "unspeakable" abuse
The prime minister has said any necessary changes will be made to the system in the wake of the abuse by a father who raped his two daughters.
Gordon Brown said people were "outraged" by the "unspeakable" abuse perpetrated against the women.
His comments follow demands by MPs in Sheffield to know how the father's actions went undetected by agencies.
The 56-year-old Sheffield man was jailed for life after fathering nine children by his daughters.
An independent review is investigating the contact health professionals, police and social services had with the victims.
During Prime Minister's Questions at the House of Commons, Gordon Brown said: "People will want to know how such abuse could go on for so long without the authorities and the wider public services discovering it and taking action.
I can't imagine a better definition of being evil than torturing your own children in this abusive way
Sheffield Hallam MP Nick Clegg
"If there is a change to be made in the system and the system has failed, we will change the system."
Meanwhile, Sheffield MPs Nick Clegg and David Blunkett have called for the inquiry to uncover any failings in the system.
The father, who admitted 25 rapes, was sentenced to a minimum term of 19-and-a-half years by judge Alan Goldsack QC, who said the case was the worst he had seen in 40 years.
The attacks led to 19 pregnancies. Nine of the children were born, two of whom died on the day of their birth.
The other 10 pregnancies were miscarried or aborted.
Nick Clegg, Lib Dem leader and Sheffield Hallam MP, said: "I can't imagine a better definition of being evil than torturing your own children in this abusive way."
Asked by BBC News "Where were the medical professionals? Where were the social workers?", Mr Clegg answered: "Yes, we don't know. Those are the big questions that need to be asked.
"The other questions are for people at school. The girls went to school. Did they not notice anything?
Nick Clegg said the abuser 'moved from place to place'
"The girls were in and out of hospital - did they not notice anything?
"They've got someone from outside to look at it independently and make sure that we know if there have been any major failings in the system that those are brought to light."
Labour's Sheffield Brightside MP and former Home Secretary David Blunkett said: "Those who at least made an effort to do something should not be the ones who are pinpointed - it is those who did not who should examine their conscience."
Sheffield Crown Court heard the abuse started when the women were pre-pubescent.
The father moved the family around, including Sheffield and Lincolnshire, to keep them isolated and to avoid detection.
In 1996 while the family were living near Skegness the youngest daughter went to hospital and received a blood transfusion.
In 1997 the family came to the attention of Lincolnshire Police after an allegation was made of incestuous rape but no action was taken.
The court heard that none of the doctors, nurses or social workers the victims saw looked into why they kept getting pregnant.
Social services criticised
The case ended two weeks after Haringey Council in London came under fire over the death of Baby P.
The 17-month-old boy died in August last year in a blood-stained cot after months of abuse, despite 60 visits from authorities over eight months.
Children's Secretary Ed Balls has ordered an inquiry into Haringey's child welfare services.
Baby P's mother, her boyfriend and her lodger are due to be sentenced on 15 December after being convicted of causing or allowing the child's death.
Peter Duxbury offered sympathy to the victims
James Baird, representing the father in the Sheffield abuse case, criticised social services in both Sheffield and Lincolnshire, where the family had lived.
He said there had been many hospital appointments where staff had "accepted the complainants' case that the father of their children was not their father".
Jayne Ludlam, director of young people's services Sheffield City Council, confirmed a Serious Case Review had been launched, to be led by former civil servant Professor Pat Cantrill.
Peter Duxbury, director of children's services at Lincolnshire County Council and chairman of the Lincolnshire Safeguarding Children Board, said since the events child protection systems had been improved.
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