Number 10 has warned against a "trial by Twitter" over sexual abuse claims after David Cameron was handed a list of suspects on live television.
The Prime Minister's spokesman said in a briefing: "We should not have a trial by Twitter. People should not be throwing about unsubstantiated allegations."
He added: "There are lots of accusations flying round and many accusations on the internet. We need to be very careful.
"If there are allegations, they need to be looked at properly in the right way by the relevant authorities. People need to be cautious of the fact that naming names could have implications for future criminal prosecutions."
The fresh warning followed Mr Cameron expressing fears about a "witch hunt" of gay people after he was questioned about the claims during an interview.
He was given a list of suspected paedophiles by Phillip Schofield when he appeared on ITV's This Morning, where he was appearing to talk about dementia.
Schofield, who said he had found the names on a quick trawl of the internet, came under fire after accidentally exposing the list on camera as it was handed to the PM.
Mr Cameron did not look at it and put it on the table, before raising concerns about internet speculation over who might be embroiled in historic cases.
"There is a danger if we are not careful that this can turn into a sort of witch hunt, particularly about people who are gay, and I'm worried about the sort of thing you are doing right now, taking a list of names off the internet," he told Schofield.
"If anyone has any information about anyone who's a paedophile, no matter how high up in society they are, that is what the police are for."
He added: "I've heard all sorts of names bandied around and what then tends to happen is everyone sits around and speculates about people, some of whom are alive, some of whom are dead."
Mr Cameron insisted the Government was moving quickly to investigate new claims, which include allegations that a senior Conservative from the Thatcher era was involved in abuse in North Wales.
One of the alleged victims in that case, Steve Messham, has claimed he was regularly taken to a hotel and sold for sex - including to the politician.
The Prime Minister described the allegations as "extremely serious" and pointed out the Government had this week launched an inquiry into the Welsh care home scandal.
There are now a series of different investigations into historic allegations, with two into the Welsh case and others sparked by the Jimmy Savile scandal.
The Prime Minister defended the move not to set up a single inquiry to look at all the claims, insisting this would not necessarily be quicker.
"The idea that if you had one mega-inquiry that you would speed everything up, I'm not sure is true," he said.
"I don't rule out taking further steps. I want the Government to be absolutely on top of this, I don't want anything to be covered up, I don't want any information to be held back. If there are more things we have to do, we will do them.
"But we always have to remember it's very easy for governments just to stand up and say, 'Here's a new inquiry.' What we've got to do is get to the truth as fast as we possibly can."
Conservative MP Stuart Andrew, who was a councillor in Wrexham at the time of the original inquiry in the 1990s into the Welsh abuse, accused Schofield of mounting a "very cheap stunt".
Mr Andrew said: "It is not acceptable to take a cheap shot on something that is so fiercely sensitive. Anybody who has got any allegations to make must make them to the police, so they can be properly investigated."
Schofield later said in a statement: "If any viewer was able to identify anyone listed, I would like to apologise and stress that was never my intention.
"I was not accusing anyone of anything and it is essential that it is understood that I would never be part of any kind of witch hunt.
"Unfortunately, there may have been a misjudged camera angle for a split second as I showed the Prime Minister some information I had obtained from the internet.
"I asked for his reaction to give him the opportunity to make a point which he very clearly made about the dangers of any witch hunt."