David Cameron has warned that accusations of paedophilia against senior Conservative politicians risk creating a witch-hunt, particularly against gay people.

The prime minister made his comments after he was confronted on daytime television with a list of names circulating on the internet of Tory politicians possibly involved in child sex abuse claims. The piece of paper was accidentally briefly flashed on air.

Speaking on ITV1's This Morning, Cameron appealed to anybody with information to contact the police but raised concerns over the internet speculation about who may 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 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."

The presenter, Phillip Schofield, passed Cameron a list of names he had gathered from the internet, saying: "You know the names on that piece of paper, will you be speaking to these people?"

Cameron replied: "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."

Schofield later apologised for potentially revealing the names, blaming a "misjudged camera angle". He said: "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."

The Conservative MP Rob Wilson wrote to Ofcom chief executive Ed Richards urging him to investigate whether This Morning breached the broadcasting code "when Mr Schofield revealed the names of certain individuals in connection with allegations of child abuse and paedophilia against Conservative politicians".

Under Ofcom's code, broadcasters are obliged to seek a response from individuals who are the subject of significant criticism or allegations of wrongdoing.

ITV said: "It is extremely regrettable that names may have been very briefly visible as a result of a misjudged camera angle, although most viewers would not have been able to read the list. As Phillip has stressed, the programme was not accusing anyone of anything."

On BBC's Question Time on Thursday night, Chuka Umunna, the shadow business secretary, said Schofield's behaviour was "foolish, stupid and amateur". He accused the presenter of trawling through the internet and said such behaviour flew in the face of what victims wanted – a serious investigation.

Baroness Williams added: "I thought the prime minister behaved with very great dignity and very great restraint."

Allegations that senior Conservative politicians may have been involved in abuse at children's homes in north Wales triggered two separate inquiries this week. They are the latest in a number of inquiries set up over recent weeks after a slew of historic child sex abuse allegations involving the BBC, care homes and Whitehall surfaced, beginning with revelations about the BBC presenter Jimmy Savile.

The home secretary, Theresa May, announced on Tuesday that the incoming director general of the new National Crime Agency, Keith Bristow, would head a team looking at how North Wales police investigated allegations of child abuse in the 1970s and 1980s, amid claims that they failed to take complaints seriously. A high court judge, Mrs Justice Julia Wendy Macur, would examine the scope and conduct of the previous Waterhouse inquiry into the abuse.

The former children's minister Tim Loughton used an open letter to the prime minister on Thursday to urge him to launch a single, wide-ranging judicial inquiry into child abuse for fear of "drowning" in separate inquiries. The Conservative MP for East Worthing and Shoreham said it was time to set up an overarching inquiry "into what went wrong across a whole range of institutions".

Cameron did not rule out one "mega inquiry" in future, but said he was interested in getting the information in the quickest way possible. He told This Morning: "The real question is would that help us get to the truth quickly. The idea that if you had one mega-inquiry that you would speed everything up – I'm not sure it's true. 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 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 to stand up and say: 'Here's a new inquiry'. What we have got to do is get to the truth as fast as we possibly can."

The National Society for the Prevention of Cruelty to Children said there should be an overarching review into "lessons learned" to pull together the findings and lessons learned once all the inquiries were completed.

Labour MP Ann Clwyd backed the setting up of a super-inquiry as she called for a shelved report detailing rape and torture at children's homes in north Wales to be published. The MP for Cynon Valley told the Commons she had seen the report by John Jillings, commissioned by Clwyd county council in 1994, which was never made public because of legal concerns.

In a question to Commons leader Andrew Lansley, Clwyd said: "Can I ask that the Jillings report be published? I saw it. I wasn't supposed to see it. It was shown to me. I saw it at the time. It was subsequently pulped by the then Clywd county council because they were afraid of the attitudes of the insurers. I would say please get the Jillings report published because it shows buggery, rape, bestiality, violent assaults and torture."

Shadow Commons leader Angela Eagle also demanded a single inquiry into claims of abuse. She said: "There are now 13 separate, overlapping inquiries into sexual abuse of children and young people. Would it not be more appropriate for a single, overarching inquiry to be established so we could get at the truth?"

Lansley said he would ask May to look again at whether a single super-inquiry was needed.

"As the home secretary made clear, we are not ruling such an overarching inquiry out. But we must be very clear, this is not an issue of principle, this is an issue of what works best in practice. There are a range of inquiries that have powers and ability to investigate specifics. There is a danger … to substitute those with some kind of overarching inquiry, the scope of it and scale of it will impede us making progress."

Jillings said on Wednesday that his inquiry 18 years ago had focused on allegations of abuse by members of staff at the homes but found no evidence a senior Tory had been involved.

He told BBC Radio 4's World At One: "The people that our investigation focused on – because these were the people the children spoke to us about – were staff members."

Andrew Flanagan, the NSPCC chief executive, said: "There is a need to ensure that the public has confidence that the numerous inquiries under way will result not only in justice for people who have suffered abuse, but in improvements to the way we protect today's children. It's vital any review puts the needs of victims right at its heart and ensures recommendations are implemented in full.

"Whilst the cases of Jimmy Savile, Bryn Estyn children's home, and others, may appear to be quite different there will be similar failings, both from institutions and individuals."

He said "public and political opinion will shift in a similar way to that seen following the death of baby Peter Connelly," who died in 2007 after horrendous abuse at home.

"We must maintain this momentum and use this opportunity to fundamentally change how we help children and young people to talk about abuse," Flanagan said."