Serial killer Levi Bellfield is said to have confessed to the murders of Lin and Megan Russell in Chillenden.
The "detailed" confession could clear convicted killer Michael Stone, who is serving life for the notorious killings.
The Gillingham resident has been in prison for more than 20 years over the deaths of the mother and daughter in 1996, who were bludgeoned in a country lane.
Scroll down for video
But at a press conference today in London, Stone's lawyer Paul Bacon revealed Bellfield had confessed the crimes to a fellow inmate - including divulging information not already in the public domain.
Michael's sister Barbara Stone, who lives in Chatham, says Bellfield had revealed “intimate” unpublished details of the Russell crime scene while in prison, putting fresh doubt on her brother’s conviction.
Stone has always proclaimed his innocence and his legal team has now approached the Criminal Cases Review Commission (CCRC), which investigates suspected miscarriages of injustice.
In a statement, a spokesman for the commission said: "The case of Michael Stone is currently under active investigation at the Criminal Cases Review Commission and we are looking into a number of issues."
The 56-year-old was convicted of the savage hammer attack on Mrs Russell, 45, and six-year-old daughter in an isolated country lane in Chillenden, near Canterbury.
Josie Russell, then aged nine, was left for dead but made a full recovery.
Ms Stone added they would also be calling for the police to launch a full inquiry.
Mr Bacon said the Russell murders fitted the "modus operandi" of Bellfield. He also claimed to have a witness who saw Bellfield close to the scene of the murders.
He said: "We have now received evidence of a full confession by Levi Bellfield to the Russell murders.
"In the confession, Bellfield describes how he came across Lin Russell and her two children, how he attacked them with a hammer and his motivation for the killing.
"The confession is detailed and has a number of facts which are not in the public domain."
He continued: "We have now conducted a full review of the case papers and have an independent witness who saw Levi Bellfield close to the scene of the murders at about the time they were committed.
"And importantly we have identified forensic material from the scene of the murders which corroborates the confession made by Levi Bellfield.
"The Russell murders by Levi Bellfield fits perfectly with his modus operandi. He is a man who is known to attack and murder women in remote locations and his weapon of choice is a hammer.
"This material, including the detailed confession, is now before the Criminal Cases Review Commission.
"We are of the view that this evidence must as a matter of urgency be brought before the Court of Appeal.
"We know that Levi Bellfield will deny the confession and will make up counter allegations but we also know that Levi Bellfield is very manipulative."
Mr Bacon added: "Finally, we have concerns about the Kent Police investigating this and would ask that an independent police force look at the investigation and in particular the fresh evidence we have presented to the Criminal Cases Review Commission."
Speaking after the press conference, Ms Stone said the development had given her family hope for her brother's release.
He said: "I'm overwhelmed and feel quite positive. If this evidence was available at the time of the trial it definitely would have made a difference to the verdict the jury arrived at.
"I would urge the CCRC to deal with it quite quickly and make a referral to the Court of Appeal as soon as possible."
She also spoke of the emotional anguish caused by her brother's incarceration, and her tentative faith in the justice system.
She continued: "It's been 20 years since my brother's been in prison and during that time, we've had a lot of disappointment.
"The quality of the evidence without doubt is really good and should ensure my brother's freedom, but there's always that little niggle that it's not going to be quite good enough.
"I won't allow myself to believe for definite he's coming out but we're very very hopeful. This is the most hope we've had for many years.
"Every day I wake up and the first thing I think about is that he's in a prison cell and I'm walking around.
"He's confined in prison but for me it's a mental confinement and it never goes away. It affects everything I do in life and the way I am."
Referring to the investigation that led to her brother's conviction, she added: "I'm thoroughly disappointed with Kent Police. I think the original investigation was seriously flawed.
"I won't allow myself to believe for definite he's coming out but we're very very hopeful. This is the most hope we've had for many years" - Michael Stone's sister, Barbara
"I don't believe the investigation was of a standard that we should expect of our UK judiciary system."
Kent Police have since said it is "unfair" on the victims in the case to continue to question and re-release details on the investigation and Stone's conviction.
Bellfield is serving a full-life term for the murder of Milly Dowler.
He finally admitted in January last year that he killed the schoolgirl after abducting and raping her.
At the same time, he revealed he was also behind a string of other brutal attacks – including two murders.
There was speculation he could have been responsible for the Russell killings.
The nightclub bouncer and wheel-clamper would accost women as they walked home, bludgeoning then with a hammer from behind.
Ms Stone has spoken to her brother behind bars at Durham’s Frankland Prison where Bellfield is also being held.
She said: “Mick is very positive. He is very hopeful.”
Stone, a heroin addict with a criminal history, was arrested a year after the attacks.
He was convicted in October 1998 after the jury believed the thrust of the prosecution’s case based on three prison inmates who claimed he had confessed. His team challenged the conviction and a retrial was ordered.
But one of the inmates, Damien Daley, “a self-confessed liar”, stuck to his story saying Stone had gone into horrific detail about the murders.
In summing up the judge, said: “The case stands or falls on the alleged confession of Damien Daley.”
In 2001, Stone, formerly of Skinner Street, was once again found guilty and handed three life sentences.
Stone has since failed in two appeal bids.
A BBC2 documentary, The Chillenden Murders, broadcast in June, concluded there was no forensic link to Stone at the scene.
Stone has consistently protested his innocence.
Stone’s solicitor Paul Bacon said today: “We have lodged new evidence with the Criminal Case Review Commission with a view to asking the Court of Appeal for a review.”