Michael Stone’s convictions for murder and attempted murder will not be referred to the Court of Appeal despite serial killer Levi Bellfield allegedly confessing to killing Lin Russell and her daughter Megan.

The Criminal Cases Review Commission (CCRC), an independent investigator of potential miscarriages of justice, has reviewed Stone’s case and concluded there is “no real possibility” the Court of Appeal would quash his convictions.

But Stone’s barrister Mark McDonald said the CCRC’s announcement on Thursday was “utterly astonishing”, as he claimed Milly Dowler’s killer Bellfield has “made numerous statements confessing” to the Russell murders.

Stone is serving three life sentences for the murders of Ms Russell, 45, and her six-year-old daughter, who were found bludgeoned to death in Chillenden, Kent, in July 1996.

Ms Russell’s other daughter, Josie, then nine, suffered severe head injuries in the attack and the family’s dog, Lucy, was killed.

Last year, Bellfield, who is serving two whole-life orders, claimed responsibility for the murders before later retracting his statement.

In April, lawyers acting for Stone claimed that Bellfield had written and signed a fresh confession to the murder.

A CCRC spokesperson said: “Where a jury has chosen to convict a defendant, the Court of Appeal will only interfere if it can be shown that the conviction is unsafe.

“Our role is not to retry a case but to consider whether there is new evidence or argument which may lead to a real possibility that the Court of Appeal would quash the conviction.

“We have identified no new evidence or information that raises a real possibility that Mr Stone’s conviction would not be upheld upon a reference to the Court of Appeal.”

But Mr McDonald claimed the CCRC is “not fit for purpose”.

He told the PA news agency: “We’re saying that the test that they apply is simply too high – if an innocent man can’t get out of jail when someone else has confessed then the whole system is falling apart.

“Frankly, it’s not a good place to be innocent in this country at the moment, I’ve been a barrister for 27 years and I find it right now that the system is not set up for people who are innocent.

I've got about five statements from Bellfield saying 'I murdered the Russells'

“The CCRC have refused to undertake any comparison with Levi Bellfield’s DNA, even though we know there was a partial DNA found at the crime scene. This is staggering, given that Levi Bellfield has confessed to the crime.

“The CCRC have refused to interview any witnesses we’ve put forward that corroborate Bellfield’s confession – again, staggering.

“The CCRC have effectively put the burden upon Michael Stone to prove that Bellfield has committed the crime. How on Earth could he ever do that?

“I’ve got about five statements from Bellfield saying ‘I murdered the Russells’.

“I paraphrase, obviously, but these are signed statements by him saying that he is responsible for the murder, he even told the police in interview under caution that he murdered the Russells, and still they won’t refer this matter to the Court of Appeal.

“So what more can Bellfield do, what more can he possibly do to say he is responsible?”

He said that the CCRC “don’t believe” Bellfield because “in the past he has confessed to other crimes and the police don’t believe him”.

The CCRC, which investigates cases in England, Wales and Northern Ireland, said it had examined a “substantial number of documents relating to Mr Stone’s case, including reports of alternative events and suspects, court transcripts and judgments, files from police forces and the Forensic Science Service”.

It added that “interviews took place with officers from several police forces, and forensic tests were carried out” as part of the review.

Bellfield was given a whole-life term for murdering Marsha McDonnell, 19, in 2003, murdering Amelie Delagrange, 22, and trying to murder Kate Sheedy, 18, in 2004.

He was already serving his sentence when he went on trial for killing schoolgirl Milly, who was snatched from the street walking home from school in Walton-on-Thames, Surrey, in March 2002.

Bellfield was found guilty of abducting and killing the 13-year-old following a trial at the Old Bailey in 2011.