After the 84-year-old's unanimous conviction on 12 sex charges involving four women - most while they were underage - police said they would look at fresh allegations that were not part of his trial at Southwark Crown Court.
Dozens more alleged victims came forward during the trial, including several in Australia, and Scotland Yard has been in touch with their counterparts in the Australian police. It is not yet clear whether they are pursuing any investigation in Harris's home country.
Richard Scorer, abuse lawyer for Slater & Gordon who represent 176 victims of Jimmy Savile, said they had been contacted by "up to a dozen people" with allegations about Harris and were considering them carefully.
The 12 women who have contacted the law firm are thought to be from the UK, New Zealand and Australia.
Mr Scorer said: "We back an over-arching inquiry into child abuse once those reports which are still outstanding are completed.
"What we have discovered in the wake of the Jimmy Savile scandal is just how deep child abuse in institutions ran and how some people were seemingly allowed to continue their sickening crimes unchallenged. It is therefore vital we do everything possible now to learn from the mistakes of the past and take this opportunity to toughen the laws around the protection of children and vulnerable adults in institutions."
Harris faces jail when he is sentenced on Friday for the offences, and his reputation is in ruins following his conviction.
The mayor of Perth in western Australia said the council was considering tearing up a plaque to Harris inlaid in the city's St Georges Terrace, while there is growing pressure for the disgraced entertainer to be stripped of his honours from the Queen.
Harris has already had his Bafta fellowship, awarded two years ago, removed.
Australian prime minister Tony Abbott said he was "gutted and dismayed" by the news of the conviction, telling ABC radio: "It's very important that we do everything we humanly can to protect vulnerable young people. Sexual abuse is an utterly abhorrent crime. It's just sad and tragic this person who was admired seems to have been a perpetrator."
Simon Danczuk, Rochdale MP, has called for the star's honours to be revoked - Harris received an MBE in the 1960s, followed by an OBE a decade later, and a CBE in 2006.
Mr Danczuk said: "I think the guy is an absolute disgrace and he is bringing the whole honours system into disrepute."