Mrs Pemberton had long been a victim of domestic abuse
A mother and son who were shot dead by her estranged violent husband in 2003 in Berkshire were let down by the "standards of basic policing".
Julia Pemberton and 16-year-old William were killed by Alan Pemberton, 48, who then turned the gun on himself, at their home in Hermitage near Newbury.
An independent review into their deaths found "significant opportunities" were missed to identify the threat.
Thames Valley Police said it "has learnt lessons from the tragic deaths".
A court order had banned Pemberton from going near his estranged wife and their property after he had made threats to kill her.
But the review, commissioned by the West Berkshire Safer Communities Partnership and published on Monday, criticised Thames Valley Police for not having a domestic violence policy in place at the time and failing to notice the warning signs.
The couple separated in September 2002 following years of his "unpredictable, demanding and controlling" behaviour.
Over the next year he made threats to kill her and the family, glued the locks on the house and scribbled threats on an affidavit applying for the injunction.
Mrs Pemberton, who was suffering from breast cancer, met the Thames Valley Police domestic violence co-ordinator a number of times and had an alarm fitted to the home.
But Pemberton was never interviewed by police or charged with any offence.
The 200-page report's authors said: "It is our view that on a number of occasions Julia did not receive a competent police response.
"We believe she was let down by the standards of basic policing, record keeping and follow-up.
"There is evidence of instances when police officers did not attend the scene, thoroughly investigate or link incidents or crimes which were reported."
At an inquest into their deaths East Berkshire coroner Peter Bedford recorded verdicts of unlawful killing and said police could not have prevented their deaths.
But Mrs Pemberton's brother, Frank Mullane, from Swindon, won an agreement - the first of its kind in the UK - to hold a review of the deaths to help shape future investigations.
Mr Mullane said: "This was not about saying sorry, it's about saying someone is at risk next week because something is broken in our police force so we have a duty to get it fixed."
The review found that "opportunities were missed" to collect evidence in the first "golden hour" after complaints of his threats to kill were received.
"Had the threat to kill been investigated as a serious crime in September 2002, the course of events that led to the death of William and Julia Pemberton in November 2003 may have been interrupted," the report said.
"Significant opportunities were missed in April and May when information was available concerning the escalating risk to Julia and William, which may have led to a more informed police response at a critical time.
"We have concluded that positive intervention by Thames Valley Police in response to reported crime in the preceding 14 months may have altered the course of events.
"It is not possible to know whether positive intervention ultimately could have prevented the deaths of William and Julia."
In a statement, Det Ch Supt Andy Taylor, said: "There is no doubt in my mind that Thames Valley Police could have, and should have, provided Julia Pemberton and members of her family with a much better service than the one they received.
"We agree with the report that they did not receive an effective police response and we apologise for the distress this has caused the family."
He added that the force - which deals with about 1,000 domestic violence incidents a month - was "not complacent" and made "significant improvements" in how it deals with such cases including a force-wide policy on domestic abuse.