Updated

Speculation about a political figure from the Margaret Thatcher era alleged to be tied to Britain's child abuse scandal risks becoming a witch hunt, Prime Minister David Cameron warned Thursday after he was confronted in a television interview with names of supposed potential suspects.

Cameron has authorized two new inquiries into widespread child abuse at care homes, foster homes and other institutions for vulnerable young people in Wales in the 1970s and 1980s. One victim has alleged that previous investigations had failed to examine accusations against a senior figure within Cameron's Conservative Party at the time.

The political figure has not been named, and no official with the Conservative Party — led from the mid-1970s until 1990 by Thatcher — has ever faced charges in connection to the abuse scandal.

Allegations were raised in the wake of disclosures that renowned BBC children's TV host Jimmy Savile is accused of using his fame — and charity work that took him to schools and care homes — to abuse hundreds of young people in past decades. Savile died last year.

Police and charities say the case has been a "watershed moment," prompting adults to come forward with scores of unrelated complaints about sex abuse they claim they suffered in childhood.

During an interview Thursday on ITV's "This Morning" program, presenter Phillip Schofield passed Cameron a note bearing several names of political figures mentioned on social media sites in connection with the allegations of abuse in Wales.

"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," Cameron said, rebuking the program for highlighting the speculation.

"I do think it's very important that anyone who's got any information about any pedophile, no matter how high up in the country, or whether they are alive or dead, go to the police."

Several inquiries are under way into allegations against Savile, including a police investigation, internal reviews at the BBC and a study by the National Health Service into the presenter's charity work. Cameron this week ordered separate investigations into a previous public inquiry into the Welsh abuse cases, and a review of how police handled allegations made at the time by young people.

Some lawmakers have expressed concern that so many reviews many mean that no clear steps are established for future investigations of abuse claims. Many have called for a single, sweeping public examination of the issue.

Cameron said it is possible that Britain could hold a public reckoning, but only after current investigations are completed.

"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," he said.