Conservative MP Rob Wilson has reported ITV to the media regulator, while Schofield has been accused of being "silly and tasteless" over the action, reports Sky News.
Ofcom has confirmed that "a few" complaints have been submitted after Schofield presented Cameron with the names - supposedly linked to the Conservative Party - which he had put together after "trawling the internet" for just three minutes.
Schofield has already apologised for the incident and insisted that he was not trying to start "any kind of witch hunt".
But Wilson called on the regulator to investigate whether ITV may have broken the rules stating that any individuals must be given fair chance to respond before allegations are made on-screen.
Speaking on last night's Question Time, policing and criminal justice minister Damian Green also denounced Schofield's actions.
"I think the stunt that Phillip Schofield pulled of presenting a list of names he had taken off the internet to the Prime Minister live on television was a tasteless and silly stunt and he should not have done it," he said.
Cameron has been accused of confusing the debate by saying that discussion on the internet of an alleged paedophile ring could degenerate into a witch hunt against people who are gay.
After refusing to look at Schofield's list, he added: "I've heard all sorts of names being bandied around and what then tends to happen is, of course, everyone sits around and speculates about people.
"There is a danger, if we're not careful, that this can turn into a sort of witch hunt, particularly against people who are gay."
Following criticism of the statement, Green said that Cameron was merely warning against creating a "witch hunt".
"What the Prime Minister was warning about is that if we just start plastering names all over the place, of people against whom there may be no evidence, it may well turn into a witch hunt and clearly because of the attitudes towards gay people at the time, in the '80s, many of them are likely to be on it," he said.
But human rights campaigner Peter Tatchell told Sky News: "There is no reason why he should link the current scandals with gay people or warn of an anti-gay witch hunt. The current investigations concern paedophilia, not homosexuality."