|Edward Heath, who was prime minister from 1970 to 1974, died in 2005|
The Met, Wiltshire, Kent and Jersey police forces are conducting separate investigations involving the late MP.
The BBC understands Wiltshire Police halted an inquiry into a brothel keeper in the 1990s after she said Sir Edward was involved in child sexual abuse.
The Sir Edward Heath Charitable Foundation said it was confident he would be cleared of any wrongdoing.
The BBC's Home Affairs correspondent Dominic Casciani says claims made by the female brothel keeper, that the former PM was a client, meant that she had left herself open to prosecution.
The case against her was allegedly discontinued between 1990 and 1995 - but the woman, whose identity is known to the BBC - was later convicted of controlling prostitutes after a successful prosecution by Wiltshire Police.
She was jailed for six years after a trial which included allegations that she had supplied children as young as 13 to her clients.
It is unclear whether or not the force then went back to re-investigate the woman's original allegations against Sir Edward after she was convicted - and this is now part of a corruption inquiry by the Independent Police Complaints Commission.
The IPCC said on Monday that it would look at whether Wiltshire officers failed to pursue allegations of child abuse made against Sir Edward, who was prime minister from 1970 to 1974 and died in 2005 aged 89 at his home in Salisbury.
A retired detective has alleged that claims were made in the 1990s but were not followed up.
Wiltshire Police has declined to comment on the case, but has appealed for information regarding allegations against Sir Edward.
Wiltshire Police and the NSPCC said they had received "a number of calls" from members of the public.
They said any lines of enquiry would be passed to the relevant police force and followed up.
|Tom Watson MP|
"The victim has named Sir Edward Heath in connection with the allegation. Detectives are making initial enquiries, and will obtain a full account from the victim. The report has been notified as part of Operation Hydrant," it said in a statement.
Operation Hydrant is a nationally co-ordinated exercise to collate all allegations of historical abuse involving high profile figures.
Meanwhile, Labour MP Tom Watson said he had referred two allegations of child sexual abuse by Sir Edward to the police since 2012.
He said: "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."
He said the different approach to allegations by different forces showed the need for a national police inquiry.
|Sir Edward lost the Conservative Party leadership to Margaret Thatcher|
Operation Midland is examining claims that boys were abused by a group of powerful men from politics, the military and law enforcement agencies at locations across southern England and in London in the 1970s and 1980s.
It has focused on the Dolphin Square estate in Pimlico, south-west London.
Separately, the States of Jersey Police has confirmed Sir Edward forms part of Operation Whistle - its investigation into historical allegations of abuse in Jersey.
|Haut de la Garenne boys home, Jersey|
It includes 45 suspects - some of whom are dead or currently unidentified - at four institutions, and currently includes 13 "people of public prominence", the force's website says.
Friends of Sir Edward have dismissed the claims saying there is not a shred of evidence to link him to abuse.
The Sir Edward Heath Charitable Foundation, which operates the museum at Arundells, his home in Salisbury, said it welcomed the investigation.
"We wholeheartedly believe [it] will clear Sir Edward's name and we will co-operate fully with the police in their enquiries," a spokesman said.
Sir Edward led the 1970-1974 Conservative government and took Britain into what was then the European Economic Community.
He lost his leadership of the party to Margaret Thatcher in 1975 - something he never forgave her for and he refused to serve in her cabinet.
He was also a successful author, a renowned classical musician and a world-class yachtsman.
And now, apparently, prolific paedophile!