"I don't think it is for me to comment on the veracity of different allegations," she said. "I think it is right that the police should decide on the scale of the evidence and not for me to comment on live radio."
She added: "If they decide there is no evidence or the Crown Prosecution Service decide there is no evidence, then that is the way the criminal justice system works.
"We have a criminal justice system which operates within the bounds of the law. It is right that we let them pursue this and do that job for these very serious crimes, rather than us trying to pre-empt those judgments in one direction or the other."
Lord McAlpine, the Thatcher-era Tory treasurer, was smeared online following allegations of abuse made on the BBC's Newsnight programme last week, which did not name him.
Steve Messham, a former resident of the Wrexham care home at the centre of the allegations, claimed he had been taken to a Wrexham hotel and abused by a prominent Tory more than a dozen times.
But a local councillor who was also a victim of abuse at the Bryn Estyn home told the Guardian he did not believe Lord (Alistair) McAlpine was involved.
Keith Gregory said he thought a different member of the McAlpine family who lived locally may have been mistaken for Lord McAlpine.
A man who children at the care home believed to be a McAlpine would arrive there in an expensive car, he said.
Jimmie McAlpine, who chaired the north of England builders Alfred McAlpine Ltd, was said in his Times obituary to have an interest in vintage cars, and to have amassed "what was at one time the biggest private collection in Britain."
The Waterhouse inquiry into the abuse allegations recorded that, according to Mr Messham's statement to the police, "X (the letter used to hide the identity of the McAlpine family member) had several different motor cars and would wait for him at the bottom of Bryn Estyn Lane."
Reporters covering the inquiry at the time concluded that Lord McAlpine could not be the person referred to as the abuser because Mr Messham said his abuser was dead, whereas Lord McAlpine is alive. And when a Times reporter put Lord McAlpine's name to Messham in 1996, he said his abuser was in fact called Tom.
Another boy who originally appeared to corroborate the accusation later confirmed that he had only been shown a photograph of Lord McAlpine by a journalist subsequently, and said this was his sole knowledge of him. Lord McAlpine has strongly denied the allegations.
It came as David Cameron warned that homosexual men were at risk of a "witch-hunt" yesterday after he was confronted with a list of suspected paedophiles live on television.
ITV was heavily criticised after the presenter Phillip Schofield inadvertently exposed the list of alleged
child abusers to viewers during an interview on the This Morning programme.
A Conservative MP asked regulators to investigate whether ITV had broken the broadcasting code and Jonathan Dimbleby described Mr Schofield's behaviour as "cretinous". Downing Street warned that innocent men were at risk of "trial by Twitter", amid inquiries into alleged abuse by Jimmy Savile and other celebrities, and claims that a senior Tory figure raped a boy of 13 in north Wales in the 1970s.
Sources said Mr Cameron was unhappy about ITV's "silly stunt" and his aides felt the issue was "badly handled". During the interview, the Prime Minister did not look at the list, which Mr Schofield had compiled from the internet.
Þ Jimmy Savile's former chauffeur and flatmate has been arrested over abuse allegations. Ray Teret, 71, was detained at his home in Altrincham, Cheshire, on suspicion of rape. A 61-year-old arrested at the same time was also being questioned on suspicion of rape. Police said the allegations were not linked to the inquiry into abuse by the late DJ.
