Announcing its decision the CCRC 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. Neither can such a real possibility arise from the accumulation of multiple unsubstantiated allegations."
The Statement concluded: "The Commission is satisfied that nothing in the submissions made by and on behalf of Mr Bamber or any issues raised in the recent documentary can, either individually or cumulatively, give rise to a real possibility that the Court of Appeal would find any of Mr Bamber's convictions to be unsafe."
Bamber was informed of the decision at Full Sutton prison where he is being held.
In a statement issued by Bamber's supporters, the convicted killer said: "I shall continue to campaign to prove my innocence in every way I can. I am very shocked and extremely disappointed.
"It is illogical that the fresh evidence presented to them regarding the sound moderator has not persuaded the commissioners that this material 'may have' affected the jury's decision had they been presented with it at trial."
Bamber's lawyer Simon McKay said: "He is obviously very disappointed but remains determined to carry on the fight to clear his name.
"In my view the Commission have not applied the proper test for determining whether a case should be referred back to the Court of Appeal.
"To be clear: four independent and supremely qualified experts provided opinions that fundamentally undermined the Crown case against Mr Bamber and the safety of the convictions.
"The evidence was credible, inherently believable and gave rise to cogent admissible grounds of appeal that may have affected the jury's verdict.
"This is sufficient for the case to be referred back: whether the conviction is in fact subsequently quashed is a matter for the Court of Appeal. The Commission may have usurped the court's function."
He went on: "I will now be considering a judicial review of the Commission's decision.
"In the final analysis, whatever the notoriety that surrounds this particular case, whatever the public perception, the law applies equally to Jeremy Bamber as it does to all of us.
"The fight to clear his name will endure until justice prevails."
It is the second time the CCRC has carried out a review into Bamber's case and today's decision brings to a conclusion its longest running case.
Bamber was convicted of five counts of murder on 28 October 1986 and was sentenced to life imprisonment.
His first application for an appeal was rejected in 1988 and then again the following the year.
He subsequently applied to the Home Office for a review of his conviction which passed the responsibility to the then newly formed CCRC.
The case was referred to the Court of Appeal in 2001, but the original conviction was upheld.
