A man who is seeking to overturn his conviction for the murders of Lin and Megan Russell has had his latest appeal bid turned down.
Michael Stone has twice been found guilty of murdering the mother and daughter in Chillenden, Kent, in 1996.
His legal team made an application to the Criminal Cases Review Commission (CCRC) to refer Stone's case for appeal following fresh evidence.
The case was provisionally rejected, which his lawyers can challenge.
They have until 2 December to persuade the CCRC that its "provisional decision not to refer the case for appeal is wrong and should be changed".
Lawyer Paul Bacon said an application was made to the CCRC in 2017 based upon "information that we received from a prisoner who was friendly with Levi Bellfield," along with other fresh evidence.
He said the serial killer, convicted of murdering Milly Dowler, made a "full and frank admission" to the killings in "conversations had over a number of months"
Bellfield told BBC Wales in 2017 he was not responsible for the murders and denied making a confession.
Lin Russell and her daughters Megan, six, and Josie, then nine, were accosted as they walked along a country lane, before being bound, blindfolded and bludgeoned with a claw hammer.
Josie survived with serious head injuries and brain damage.
Stone was first found guilty of two counts of murder and one of attempted murder in 1998 and again in 2001, after the Court of Appeal quashed his conviction due to doubts over a prosecution witness and ordered a re-trial.
An earlier application to the CCRC in 2010 was rejected and an attempt to seek a judicial review of the decision also failed.
The commission said it carried out a "detailed investigation" into the latest application but was "not at this point minded to refer the case for appeal".
Mr Bacon said he would visit Stone in prison next week and "then send a response back".