The former prime minister was named yesterday in connection with inquiries carried out by detectives in London, Kent and Jersey.
On Monday, Wiltshire Police appealed for potential victims and witnesses to come forward after the late politician became the most high-profile figure embroiled in historical child sex claims.
Reports subsequently emerged that Sir Edward is being looked at as part of Operation Midland, a Scotland Yard inquiry into claims a VIP paedophile ring operated in the 1970s and 1980s.
The Metropolitan Police has not confirmed the claims. A spokesman said: “We are not giving a running commentary on Operation Midland.”
The States of Jersey Police (SoJP) confirmed the former prime minister features in Operation Whistle, an inquiry into alleged historical abuse on the island.
Operation Whistle was launched in June as part of Operation Hydrant, a UK-wide co-ordination of sex abuse investigations.
Meanwhile, Kent Police said yesterday it had received a report of a sexual assault in the east of the county in the 1960s.
A spokesman said: “The victim has named Sir Edward Heath in connection with the allegation. Detectives are making initial inquiries and will obtain a full account from the victim.”
Wiltshire Police said its officers and the NSPCC had received “a number of calls” following appeals for information.
The force said: “The investigation team will be reviewing the information and following up any lines of inquiry as a result.”
A spokeswoman said that they were unable to confirm how many people had made contact and the “validity” of the calls was not known at this stage.
They have received a mixture of “intelligence” and “third party” calls, she added.
Sir Edward’s name was linked to paedophile claims on Monday when the police watchdog announced an inquiry into allegations a prosecution against an individual was shelved after a threat was made to “expose” him.
A woman who was in charge of a brothel had been due to stand trial, but said she would expose him.
The IPCC is also looking into whether Wiltshire Police followed up a claim made against him in the 1990s.
Meanwhile, a man claimed he was raped at the age of 12 by the former prime minister.
The alleged victim, now in his 60s, has claimed he reported being sexually assaulted by the Conservative MP in 1961 but was branded “a liar and a fantasist”.
Labour MP Tom Watson has claimed he passed information relating to two allegations of child abuse involving Sir Edward to police since 2012.
Former Conservative MP Brian Binley, who worked in Sir Edward’s office for a period of time, told BBC Radio 4’s Today programme: “I find it very difficult to believe from the Ted Heath that I knew.
“There are many unanswered questions here and I don’t think it would be right and fair to jump to conclusions about a man who served his country with dignity and with care, who was a considerable intellect, loved his music. We must be very careful. It’s easy to smear people not around.”