David Cameron has warned that accusations of paedophilia against senior Tories risked becoming a "witch-hunt" against people who are gay.
The Prime Minister appealed to anybody with information to contact the police but raised concern about the internet speculation about who might be embroiled in the scandal dating back to the 1970s and 1980s.
"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," he told ITV1's This Morning.
"I do think it's very important that anyone who's got any information about any paedophile, no matter how high up in the country or whether they are alive or dead, go to the police."
After presenter Phillip Schofield passed him a piece of paper of names he had gleaned from the internet, Mr Cameron added: "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.
"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."
The Prime Minister said the allegations being made were "extremely serious" and the Government, which has instigated inquiries this week into the North Wales care home scandal in particular, had "moved quickly to try to get to the bottom of what they are".
"If you've got any information, we are a civilised, democratic country under the rule of law, with a police force, with a justice system - go to the police," he said.
There are now a series of different investigations into historic allegations of child abuse under way, but Mr Cameron said he doubted whether a single "mega-inquiry" would help get to the truth any 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."