The disgraced entertainer was found guilty on Monday of 12
counts of indecent assault in the 1960s, 1970s and 1980s, including
girls as young as seven or eight.
The Metropolitan Police said it was considering "new allegations".
Dozens more of 84-year-old Harris's alleged victims came forward during the trial, some from his native Australia.
Police in Western Australia said there were currently no new
investigations into Harris but a Met spokesman said the UK force had
"received a number of new allegations and these are now being
considered."
'Jekyll and Hyde'
Australian Prime Minister Tony Abbott said he was "gutted and dismayed" by the conviction.
Mr Abbot told Australia's ABC radio sexual abuse was "an
utterly abhorrent crime" and added: "It's just sad and tragic that this
person, who was widely admired, seems to have been a perpetrator."
Tributes to Perth-born Harris in Western Australia could now be removed, the city's mayor Lisa Scaffidi said.
Harris started a family in the UK after emigrating from Australia in 1952
During his trial prosecutors said Harris was a "Jekyll and Hyde" character who took advantage of his fame.
The judge, Mr Justice Sweeney, said a custodial term would be
"uppermost in the court's mind" when sentence was delivered on Friday,
but he wanted to see a medical report before passing sentence.
The verdict was greeted on the front page of the Sydney Morning Herald with a full-page mugshot beneath a one-word "Guilty" headline.
Harris's photograph was splashed on front pages in his native Australia
The central allegation concerned a friend of Harris's daughter
who he had groomed and molested from the age of 13 until she was 19.
His other victims were touched or groped, sometimes at his public appearances.
Six other women also told the court about indecent assaults
Harris had carried out against them. The entertainer was not prosecuted
over those incidents but the evidence was introduced by the prosecution
as an added illustration of his behaviour.
Broadmoor visit
Harris, from Bray, Berkshire, was first questioned in November
2012 in Scotland Yard's Operation Yewtree investigation set up in the
wake of sexual abuse allegations against the late BBC Radio 1 DJ Jimmy
Savile.
Although his arrest was unconnected to Savile's offending,
the publicity surrounding that case had prompted the friend of Harris's
daughter to come forward.
Lawyers for Harris wrote to media organisations including the
BBC at the time warning them against naming their client and
threatening libel action.
When he was arrested again in March 2013 the Met did not name
Harris and he was not identified in the mainstream media until a few
weeks later.
The other women who gave evidence in court contacted police
after Harris's arrest was made public and he was charged in August of
that year.
The musician and artist was a regular on children's television
Harris was named last week in a report into the actions of Savile, which revealed he had visited Broadmoor in 1973.
Politicians and officials have faced criticism for allowing
the man whose prolific abuse sparked the Yewtree investigation
unrestricted access to the psychiatric hospital where he abused
patients.
A spokeswoman for West London Mental Heath NHS Trust, which
runs services at Broadmoor, said Harris may have been accompanied by
Savile during his visit but that he was also escorted by staff at all
times and there was "no suggestion of any inappropriate behaviour".
'Beyond belief'
One of Harris's victims, Tonya Lee, 43, said the abuse had led her to contemplate taking her own life.
Tonya Lee said she had been abused by Harris while on a visit to the UK when she was 15
The mother-of-three said: "To this day I can't go to sleep
without lying in a lounge and having the TV on. I cannot lie in a room
and try and sit with my thoughts and go to sleep."
Letitia Fitzpatrick, who gave a character reference for the
prosecution about an alleged assault, told the BBC: "It was such an
unpleasant experience that I just wanted to forget about it and move on
and not really think about it again."
Harris made no comment when he left court after the verdicts
Meanwhile it has emerged that Harris fronted a child protection
awareness video in the 1980s in which he was filmed telling children
how to say no to predatory adults.
John Cameron - head of child protection at the NSPCC - told BBC Breakfast: "The audacity of the man is beyond belief.
"Here he was, giving this pretence that he had children's
welfare at heart, but of course behind the scenes, in front of many
people, he was abusing children on a regular basis."
The charity says calls to its helpline were up by a third on Monday.
It says it has received 28 calls about Harris, including 13 people who said they had been abused by him.
He was accompanied during the trial by daughter Bindi (r), wife Alwen, and his niece Jenny (l)
Speaking after the entertainer was convicted, Det Ch Insp Mick
Orchard, said: "I want to thank the women who came forward for their
bravery, I hope today's guilty verdict will give them closure and help
them to begin to move on with their lives.
"Today's case and verdict once again shows that we will
always listen to, and investigate allegations regardless of the time
frame or those involved."
Director of Public Prosecutions Alison Saunders said it was too early to say whether Harris could face further action.
"We'll work with the police and look at any cases that they
send to us and see if there is enough evidence to bring more charges,"
she told the BBC.
Harris found fame as a singer and entertainer after starting out as an artist
He painted a portrait of the Queen in 2005 and took part in her Diamond Jubilee concert seven years later
There are calls to strip Harris of awards he has received in Australia and the UK
Harris was a mainstay of family entertainment in Britain and
his native Australia for more than 50 years. He arrived in London in
1952, becoming a fixture on TV screens as a children's entertainer,
songwriter, and entertainer, on the BBC and other networks.
'Absolute disgrace'
He is to be stripped of his British Academy of Film and
Television Arts fellowship - the TV industry's highest accolade - which
was awarded just two years ago, a Bafta spokesman said.
There are also calls for him to lose the honours awarded to him by the Queen during a lifetime in the entertainment industry.
Labour MP Simon Danczuk said: "I think the guy is an absolute
disgrace and he is bringing the whole honours system into disrepute."
A final decision on whether to revoke Harris's CBE and MBE rests with Buckingham Palace.
The Australian, who began his career as an artist, received
his CBE in 2005, the year he painted a portrait of the Queen to mark her
80th birthday.