Seven claims were found to be serious enough that, had Mr. Heath been alive, “he would have been interviewed under caution in order to obtain his account,” the police said in a statement.
Those seven were five accusations of sexually assaulting boys between the ages of 10 and 15, and two of sexually assaulting adult men, one in 1976 and the other in 1992, the police said. No victims have been publicly identified.
The wide-reaching investigation, called Operation Conifer, began in August 2015. The police said it generated 1,580 lines of inquiry and collected 284 statements, and led to the arrests of at least three people. It employed 24 people and cost 1.5 million pounds, or about $2 million.
Investigators had begun reviewing allegations against Mr. Heath when a retired police officer came forward in 2014 with information about a 1994 trial that had been “discontinued,” the police said.
The retired officer expressed concern that the trial had been stopped in order to keep the defendant from publicly claiming involvement in “supply of young boys” to the former prime minister, according to the report.
Critics have called the investigation a meandering, expensive attack on the reputation of a man who is not alive to respond. Those concerns were amplified in August 2015 when the police made a controversial televised appeal for anyone who may “have been the victim of any crime from Sir Ted Heath” to come forward.
Lincoln Seligman, Mr. Heath’s godson, said the police had not conducted a “proper investigation,” and he accused them of creating an atmosphere of presumed guilt around the former prime minister, who never married.
“If you make a mass appeal for victims, you are sure to get them — whether they are legitimate or not,” Mr. Seligman said. “Our thinking is that he will be completely exonerated. But I fear, even if he is, that damage has been done, and that seems grossly unfair.”
A representative for the Sir Edward Heath Charitable Foundation did not respond to an email seeking comment on Thursday.
Chief Constable Veale said on Thursday that investigators had refrained from commenting “publicly or privately” about Mr. Heath’s guilt or innocence. He called suggestions to the contrary “misleading and inaccurate commentary.”
He added that there were “compelling and obvious” reasons to investigate claims against a man who once ran the country.
“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 public office he held,” Chief Constable Veale said. “The allegations against him were of the utmost seriousness, and from a significant number of people.”
Wiltshire Police said in a statement that they had a “legal duty” under the European Convention on Human Rights to investigate criminal allegations, even ones against the dead.
The police said their findings would be presented to the Independent Inquiry into Child Sexual Abuse, which was established in 2005 to investigate whether public and private institutions in England and Wales had taken sufficient action to protect children from sexual abuse.