Wiltshire Police have been accused of "wriggling at every single turn" after they were forced to release the only two people arrested in connection with the Sir Edward Heath child abuse inquiry.
The force has spent almost two years and more than £1 million probing claims against the former Prime Minister who died more than a decade ago.
Earlier this week the only two people to be arrested during the inquiry were told they face no further action.
The police have been on a fishing trip with this
Dr Richard Hoskins
Dr Richard Hoskins, a criminologist, who was called in by Wiltshire Police to review the inquiry, said he was now convinced there was not a shred of credible evidence against the late former Tory leader and called for it to be shut down.
He told Radio 4's Today programme: "Wiltshire Police are wriggling at every single turn here. Whenever part of their investigation falls down this is their fall back, saying there is another strand."
He added: "The police have been on a fishing trip with this. They quite outrageously, I think, stood outside Ted Heath's home and called for people to come forward."
Dr Hoskins said some of the claims that had been made against Sir Edward, including allegations of ritualistic murder, were "clearly absurd".
Lincoln Seligman, who is the godson of Sir Edward Heath, said there was no evidence the arrests had anything to do with the former Prime Minister and called for the police to publish whatever findings they had.
He said: "These arrests were used by the police as a justification for the continuation of Operation Conifer and the implication was that they were in some way connected to Sir Edward Heath.
"The police certainly did nothing to dispel that impression . Now that those people have been released without charge the police ought to make clear whether there was in fact any connection."