Levi Bellfield is said to have confessed to the murders of Mrs Russell and her daughter in Kent, for which Michael Stone is serving life sentences.
Stone’s solicitor said he has received a “genuine” four-page statement from Bellfield in which he details his involvement in the killings, which would mean his client had suffered a miscarriage of justice.
Milly’s killer is thought to be the only criminal in UK legal history to be serving two whole-life orders – for her murder, the killings of Marsha McDonnell and Amelie Delagrange as well as the attempted murder of Kate Sheedy.
Paul Bacon told the PA news agency: “I can say I have received a four-page statement from Bellfield, which is a genuine confession, it’s an absolutely astonishing breakthrough.
“I will now meet with colleagues following this remarkable development to finally, after many years, get freedom for Michael Stone. This is the evidence that will prove he is innocent.”
The alleged confession will be referred to the Criminal Cases Review Commission (CCRC).
The Sun On Sunday reported that the document included details of what he was wearing and how he made his escape.
Barrister Mark McDonald said on Twitter on Saturday: “For over 21 years I have represented Michael Stone who was wrongly convicted of the Chillenden murders.
“Tomorrow it will be announced that Levi Belfield has made a full written confession to the crimes.
“Michael Stone is innocent and must be immediately released from prison.
“Stone has been in prison for 26 years despite plenty of evidence that this is a miscarriage of justice.”
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, Mr McDonald said a bootlace found at the scene could be an “absolutely huge” and crucial piece of evidence.
He said there is “no forensic, no identification evidence at all” against Stone, and said the bootlace could yield DNA that would “undoubtedly point away” from his client.
Kent Police said its position on Stone’s conviction remains unchanged.
Detective Chief Superintendent Paul Fotheringham of Kent Police said: “Following two trials at which Stone was found guilty by a jury on both occasions, and an appeal to the High Court, Michael Stone remains convicted of the murders of Lin and Megan Russell, and the attempted murder of Josie Russell in 1996.
“Michael Stone made an application to apply for a Judicial Review in respect of his conviction in September 2012. The Honourable Mr Justice Blake ordered that permission for the application should be refused.
“The Criminal Case Review Commission commenced an extensive re-examination of the murder investigation in 2017 and has had access to all forensic evidence, documentation and exhibits from the original investigation, the review by Hampshire Police, details of the two Crown Court trials and appeals to the High Court.
“The shoelace which was seized as part of the original investigation was made available to the CCRC. All evidence from the examinations on the shoelace were recorded and disclosed to the CCRC.”