The identity of the defendant on trial is not known, but it is understood that he was not claiming to have been abused by Sir Edward himself.
The trial is thought to have been at an early procedural stage and was dropped before a jury had been sworn in.
The police officer who made the allegations is understood to have claimed that he complained about the matter at the time but said his concerns were swept under the carpet.
Last summer in the wake of criticism over South Yorkshire police's handling of the Rotherham child abuse scandal, the officer once again came forward and lodged a formal complaint.
Wiltshire Police began probing his allegations and in March this year passed the matter to the IPCC, which will now explore whether there is evidence of a police cover up and also what the police did at the time to investigate the allegations against Sir Edward.
Meanwhile a spokesman for Wiltshire Police said its detectives were now appealing for any alleged victims to come forward.
The spokesman said: "Sir Edward Heath has been named in relation to offences concerning children. He lived in Salisbury for many years and we would like to hear from anyone who has any relevant information that may assist us in our enquiries or anyone who believes they may have been a victim.
"We are working closely with the NSPCC to ensure that any victims are appropriately supported. They provide trained helpline counsellors to listen and provide assistance.
"We take all reports of child abuse, either current or that occurred in the past very seriously. Victims will receive support throughout any investigation and associated judicial process.
"If there is evidence of offences having been committed we will ensure that, if possible, those responsible are held to account through a thorough and detailed investigation.
"This includes any other parties who are identified as having been involved in child sex abuse. Some people may never have spoken out about the abuse they have suffered but we would urge them to please contact us and to not suffer in silence."
It is understood that while Wiltshire Police is not aware of any other allegations against the former Prime Minister, his name had been passed to the Metropolitan Police, which is carrying out Operation Midland, a probe into claims of a VIP paedophile operating around Westminster.
Sir Edward, who led the Conservative Government between 1970 and 1974, bought his Salisbury home, Arundells, in 1985 and lived there until his death a decade ago.
He was famously reticent about his private life and while rumours often swirled, this is the first time the unmarried former Tory leader has been name as publicly surfaced in connection with child abuse.
Last night Labour MP Tom Watson, who is fighting for the deputy leadership of the party, said: "I received information in 2012 concerning allegations of child abuse carried out by Edward Heath and a separate claim concerning Heath was made to me subsequently.
"I passed them both to the police, who have confirmed to me that at least one of those allegations is being investigated and taken seriously."
The chief Executive of the NSPCC, Peter Wanless said: "Whether abuse happened in the past, or is occurring today, whether those being accused are authority figures or not, allegations of crimes against children must be investigated thoroughly."
In a statement the Sir Edward Heath Charitable Foundation said: "We welcome the investigation by Wiltshire Police, which we wholeheartedly believe will clear Sir Edward's name and we will co-operate fully with the police in their inquiries."
- The Telegraph
