ITV News' Sejal Karial reports.
The family of murdered schoolgirl Alice Gross have demanded tougher controls to stop foreign criminals entering the UK.
Alice is believed to have been murdered by Latvian builder Arnis Zalkalns, who was convicted of killing his wife in his native country, in 2014.
An inquest jury found the 14-year-old was "unlawfully killed" in a sexually-motivated attack and her death was "consistent with compression asphyxia".
After the jury's conclusions were announced, Coroner Dr Fiona Wilcox said she will raise concerns with the Home Office over checks on foreign nationals.
She previously said evidence showed the Home Office and police "had not contributed" to the teenager's death.
Alice's family told the inquest that they "remain stunned" why a man with a murder conviction was allowed to enter the country unchecked.
Speaking outside the Royal Courts of Justice after the ruling, the Gross family said they wanted "fair and proportionate rules governing the movement of serious criminals within Europe".
"We believe if such measures been in place Alice's death might have been prevented," her father Jose Grosss said.
"We do not want to see another tragic example of a pointless and avoidable death - we do not want another family to suffer what we've been through."
Alice's body was discovered, wrapped in black plastic bin bags, in the River Brenton on September 30.
Her disappearance from her home in Hanwell, west London in August sparked what the Met said was its biggest investigation since the 7/7 bombings.
Zalkalns, who police said would have been charged with Alice's murder, was discovered hanged just after the teenager's body was found.
It also emerged that Zalkalns was questioned in 2009 on suspicion of sexual assault but police did not check if he had any prior convictions in Latvia.
In a statement after the inquest, Scotland Yard said it was now its policy to check overseas offending history if a foreign national is arrested.
"In 2009, that was not the case, in the Met or policing nationally, and this check was not done," Deputy Assistant Commissioner Steve Rodhouse, said.
"However, even if we had identified Zalkalns' conviction in that year it would not have changed the outcome of his arrest.
"We recognise that had we carried out that check in 2009 then it would have meant that our investigation into Alice’s disappearance may have identified him as a suspect slightly sooner."
Outside the Royal Courts of Justice, Alice's father Jose Gross said: "As Alice's father, losing Alice has shattered me.
"The pain of knowing I will never see, hear or cuddle her again is unbearable. This inquest has helped me face what has happened and hopefully now I will be able to properly grieve for my beautiful, loving daughter."
Her mother Ros Hodgkiss said she still found it "almost impossible to believe that our lovely daughter has been so brutally taken from us", saying she missed her "every moment of every day".
Alice's sister Nina Gross said: "I feel that it is sometimes forgotten that Alice was a real person; a kind and loving sister who deserved so much to live a full life.
"Life is broken and cold without her. Regardless of whether legal responsibility can be attributed to the State for Alice's death, I believe the State failed Alice and our family. Alice was not tragic, but what happened to her was."