It’s after “confessions” from serial killer Levi Bellfield.
The Criminal Cases Review Commission said only in July that the case would not be referred to the Court of Appeal.
But it has now agreed to carry out a further review following a request from Stone’s lawyers.
Stone has always protested his innocence over the murders, and of the attempted murder of Megan’s sister Josie.
Levi Bellfield is currently in jail for the murders of Marsha McDonnell in Hampton, Amelie Delagrange in Twickenham and Milly Dowler from Walton.
He was also jailed for the attempted murder of student Kate Sheedy in Isleworth in 2004.