The Sir Edward Heath Charitable Foundation says it is preparing a "substantial complaint" for the IPCC over allegations of sexual abuse made against the former PM.
In a statement, Lord Hunt of Wirral - chairman of the foundation - said the "deeply flawed" Operation Conifer report by Wiltshire Police leaves an "urgent need for an independent judge-led inquiry".
He said: "Sir Edward's reputation has been unfairly tarnished.
"No living person would be subject to a process which involves a trawl for accusations, followed by the publication of those accusations with no independent assessment of the 'evidence', or any details of the supposed place, time and circumstances of the alleged assaults.
"The fundamental principle that someone is innocent until proven guilty should apply to the dead as well as to the living; and no convincing evidence whatsoever against Sir Edward Heath has been produced."
He added: "It is clear the report is the result of a fishing expedition that attracted more than 100 accusations which Wiltshire Police then spent two years and £1.5m sifting through.
"Only seven were regarded as sufficient even to meet the minimal standard of credibility and justifying a police interview if Sir Edward had still been alive - and the validity of some of these is now being seriously questioned."
Lord Hunt said the foundation would be writing to the Government seeking the appointment of a retired judge to review all material collected during the two-year Operation Conifer.
"Otherwise, Sir Edward's reputation will be left forever in limbo, unjustly tarnished," he said.
The Operation Conifer report concluded that seven allegations against Sir Edward would have been sufficiently credible to justify questioning him under caution.
It did not address his guilt or innocence, because its remit was to determine whether there was enough evidence to interview the former Bexley MP - prime minister between 1970 and 1974 - under caution.
Among the allegations was the rape and indecent assault of an 11-year-old boy in 1961; indecent assault of a 10-year-old boy in 1962 and the indecent assault of a 15-year-old boy during paid sexual encounters in 1964.
Sky News Correspondent Tom Parmenter said the foundation was "not going to let this lie".
He said the IPCC complaint "will look at many of the aspects of the investigation that they [the foundation] are not happy with, including that televised appeal outside Arundells, the former home of Sir Edward Heath in Salisbury, which they described as a 'crass' and 'prejudicial' move."
On Thursday, Wiltshire Chief Constable Mike Veale defended Operation Conifer.
He said: "Sir Edward Heath was an extremely prominent, influential and high-profile person who was arguably one of the most powerful people in the world commensurate with the political office he held.
"The allegations against him were of the utmost seriousness and from a significant number of people.
"I hope people will understand that, given these circumstances, it would be an indefensible dereliction of my public duty as a chief constable not to have investigated such serious allegations against a former prime minister, even though he is deceased."