Maria Stubbings, of Chelmsford in Essex, was strangled with a dog lead in 2008 by Marc Chivers, who had already killed a previous girlfriend.
Her brother Manuel Fernandez has told ITV Daybreak that the family have been calling for a public inquiry.
He said: "This highlights issues around domestic violence with one police force but it's actually a national problem."
Repeated failures in Essex Police's handling of reports of abuse were highlighted by the Independent Police Complaints Commission (IPCC) following the cases of:
- Maria Stubbings, a 50-year-old mother of two from Chelmsford, was strangled with a dog lead in 2008 by Chivers who also killed a previous girlfriend.
- The IPCC found there was no assessment of the risk Chivers posed to Ms Stubbings and as a result she was not afforded proper protection.
- Christine Chambers, 38, from Braintree, who was shot dead in 2011, along with her daughter Shania, by her ex-partner David Oakes.
- Ms Chambers had been complaining about violence from Oakes for two years before the murders. The IPCC found the force's response was "inadequate".
- Jeanette Goodwin, 47, was stabbed 30 times by Martin Bunch, 44, in 2011, in front of her husband at her home in Southend, Essex.
- The IPCC found she received an "inadequate response" from Essex Police on the day of her murder, adding that the force did not recognise the need for urgent action.
A police force in Essex, which failed four murder victims, has been criticised over their handing of domestic violence cases.
Repeated failures in Essex Police's handling of reports of abuse were highlighted by the Independent Police Complaints Commission (IPCC).
The report follows the 2008 killing of Maria Stubbings by her ex-boyfriend Marc Chivers, the 2011 fatal shootings of Christine Chambers and her two-year-old daughter Shania by David Oakes and the murder of Jeanette Goodwin at the hands of her ex eight weeks later.
In the report, HMIC inspectors said the force took steps to improve the way it handles such cases but said further work is needed to ensure the risks to victims are properly managed.
Children as young as 11 and as old as 40 are physically, emotionally and mentally abusing their parents, according to a report out today.
The study found many parents failed to seek help because they were ashamed to admit they were suffering at the hands of a son or daughter with an alcohol or drug dependency.