The godson of Sir Edward Heath has branded the handling of allegations the former prime minister was involved in historical sex abuse a "witch-hunt".
Lincoln Seligman said Wiltshire Police had been "foolish" to believe claims made by Carl Beech about Sir Edward.
Beech, from Gloucester, made false claims of murder and child sexual abuse against a string of public figures.
The Police and Crime Commissioner for Wiltshire has called for a public inquiry to get closure for the family.
But the Home Office said: "There are no grounds to justify a review or intervention by the government.
"After careful consideration, the home secretary has concluded that the handling of this investigation remains a matter for the local police and crime commissioner."
On Monday, a jury found 51-year-old Beech, a convicted paedophile, guilty of perverting the course of justice. On Friday he was jailed for 18 years.
Sir Edward Heath was Conservative prime minister from 1970-1974 an MP for 51 years until 2001, representing the outer London seat of Bexley, and later Old Bexley and Sidcup.
Wiltshire Police said Beech was one of 40 people who had made allegations against Sir Edward, who was living in Salisbury, Wiltshire, before his death in 2005.
"At no time did anyone from Wiltshire Police speak to or take statements from Carl Beech in relation to Operation Conifer [the force's own investigation]," the force said.
"All information from Carl Beech regarding Operation Conifer was provided to Wiltshire Police by the Metropolitan Police's investigation Operation Midland which was established in 2014."
Wiltshire Police and Crime Commissioner Angus Macpherson said his force had "no alternative" but to investigate.
But Mr Seligman said: "I hesitate to use the word witch-hunt - but this was a witch-hunt.
"I find it rather extraordinary that any government can allow this unresolved matter to sit on the file of a former prime minister."
He said he wanted the circumstances of the £1.5m investigation by Wiltshire Police independently reviewed by a judge.
"I think you can't legislate against gullibility but you would hope that this might lead to the police being a bit more cautious over who they choose to believe," Mr Seligman said.
His concerns were echoed by Dr Richard Hoskin, a criminologist brought in to review parts of the Metropolitan Police's Operation Midland - which looked at allegations sexual abuse by a "VIP ring" - and others from Operation Conifer, which was launched in 2015.
Dr Hoskin said: "There's no doubt in my mind that, if Carl Beech had not pushed his fantasies, Sir Edward never would have been investigated."
He said there never was any "substantial evidence" against him, describing police as showing "collective gullibility".
But Operation Conifer concluded, if he had still been alive, Sir Edward would have been interviewed under caution over seven of the claims, although detectives stressed no inference of guilt should be drawn from that.
The expert said he was told the then Chief Constable of Wiltshire, Mike Veale, had discredited his report.
"Veale told the officers the report was going to be put in a filing cabinet in Swindon and that was going to be the end of the matter and it would never see the light of day, despite many recommendations I made in my reports," said Dr Hoskin.
"I wasn't happy with that and they even asked me at one point to alter the report to fit their pre-judgement, and again I refused to do that.
"When they continued to sit on it I went public and I felt in the national interest the public had to know what was going on."
In a statement Mr Veale denied asking for any report "to be changed or concealed".
"Given the well-documented oversight of Operational Conifer, including independent scrutiny, I believe it is inconceivable that a report commissioned by the Wiltshire Police from an independent source would have been suppressed, withheld or concealed.
"The suggestion that this has happened is, quite frankly, risible."
Wiltshire Police said all information from Carl Beech regarding Operation Conifer was provided to it by the Metropolitan Police's investigation Operation Midland, which was established in 2014.
It said Beech's allegations were considered to contain "undermining evidence" and a decision was taken not to pursue further inquiries into his allegations.
Police commissioner Mr Macpherson said: "Operation Conifer was deemed by an independent review to have been reasonable and proportionate and I remain satisfied that is still the case.
"A sharply-focused statutory inquiry, with powers to question witnesses and scrutinise documents, can now be the only way the small number of remaining allegations against Sir Edward can be discounted or given credence.
"Only the government can initiate that inquiry and provide those individuals who made the allegations with closure, while also answering the calls of Sir Edward's family and friends who seek to clear his name.
"I have pressed successive home secretaries on this and believe the government should act without further delay."