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."
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France Foreign Minister called for the action after a meeting the six European foreign ministers in Berlin.
He said that he would put himself forward if a fresh contest is held amid growing calls for him to stand down within the party.
Pet owners and cat lovers are being warned to stay on high alert after the so-called Croydon Cat Killer appeared to strike in another city.