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Lawyers for killer Michael Stone have called for his case to be reopened in the wake of the Levi Bellfield conviction.
They believe Bellfield, found guilty today of abducting and murdering schoolgirl Milly Dowler, could be a suspect in the killing of Lin and Megan Russell in 1996.
Lawyer Paul Bacon said police should now re-examine the case.
Speaking after Bellfield's conviction at the Old Bailey, he said: "Police do need to say 'if we got it wrong, we got it wrong.'
"They need to be able to say 'let's try and make sure we got the right person.'
"There's no evidence other than the alleged confession by Michael Stone."
Stone, formerly of Skinner Street, Gillingham, was convicted of the killings and the attempted murder of Josie Russell in 1998 and again at a retrial three years later.
He is serving three life sentences for attacking Mrs Russell and her two daughters in Chillenden, near Canterbury, in 1996.
The Criminal Cases Review Commission turned down his third appeal against the convictions in October last year.
Stone's sister Barbara, who lives in Chatham, has campaigned for his freedom since he was jailed as she believes her brother is innocent.
She previously said: "I feel for the Russell family and it's most unfortunate that the one thing which would make me happy would cause them stress, but my brother is not the murderer so it means the person is still out there."
Convicted killer Levi Bellfield was found guilty today of abducting and murdering schoolgirl Milly Dowler.
The 13-year-old disappeared in Walton-on-Thames, in Surrey in 2002 while she walked home from school.
In 2008, Bellfield, who is now 43, was convicted of murdering two students and the attempted murder of a third.