Jeremy Bamber's convictions for murdering five of his relatives more than 25 years ago will not be referred to the Court of Appeal.
Bamber, 51, serving a whole life term for the killings in 1985, has always protested his innocence and claims his schizophrenic sister Sheila Caffell shot her family before turning the gun on herself in a remote Essex farmhouse.
The Criminal Cases Review Commission said that despite a lengthy and complex investigation, it "has not identified any evidence or legal argument that it considers capable of raising a real possibility that the Court of Appeal would quash the convictions".
The Commission said this was its final decision in its longest-running case. It said: "Matters of pure speculation or unsubstantiated allegation constitute neither new evidence nor new argument capable of giving rise to a real possibility that the Court of Appeal will quash a conviction."
In 2009 Bamber lost a Court of Appeal challenge against the whole-life sentence. He has twice lost appeals against conviction.
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