David Cameron is facing serious questions over how his plan for automatic internet “porn filters” in every British home would work - after he suggested that topless images such as those used on The Sun’s page three would be still be accessible online.

The Prime Minister used a major speech to set out a raft of reforms to protect children from “poisonous” pornography websites which, he said, were “corroding childhood”. He announced that internet service providers had agreed to introduce family-friendly filters that automatically block pornography unless customers chose to opt out.

But his proposals were criticised by anti-censorship groups, who warned that sites about sexual health and sexuality could inadvertently get caught up in the ban.

Significantly, Mr Cameron admitted there would be “problems down the line” with the system – and appeared to rule out “soft” or written pornography from the scheme entirely.

Separately, the former head of the Child Exploitation and Online Protection centre (CEOP), Jim Gamble, said Mr Cameron’s plan to tackle child abuse images by removing results from search engines like Google would be “laughed at” by paedophiles.

“There are 50,000 predators...downloading abusive images on peer-to-peer, not from Google,” he said. “Yet from CEOP intelligence only 192 were arrested last year. That’s simply not good enough.

“We’ve got to attack the root cause, invest with new money, real investment in child protection teams, victim support and policing on the ground. Let’s create a real deterrent. Not a pop-up that paedophiles will laugh at.”

Mr Cameron laid out a multi-pronged approach to tackle the proliferation of both legal and illegal pornography on the internet, saying that the problem was “too big to ignore”.

Under his proposals, by the end of next year all households will have to “opt out” of automatic porn filters, which would come as standard with internet broadband and cover all devices in a house. Possession of the most extreme forms of adult pornography will become an offence, while online content will have the same restrictions as DVDs sold in sex shops.

To tackle child abuse images, search engines have been told they will have to redact results from specific searches, while anyone accessing websites shut down by the police for containing such images will see a message warning them that what they were doing was illegal.

But in interviews after his speech, Mr Cameron seemed unclear of exactly which legal sites should be banned by the new filters - and accepted that the technology still had weaknesses.

Speaking on the BBC’s Jeremy Vine programme, Mr Cameron said what would be included in the filters would evolve over time. “The companies themselves are going to design what is automatically blocked, but the assumption is they will start with blocking pornographic sites and also perhaps self-harming sites,” he said.

“It will depend on how the companies choose how to do it. It doesn’t mean, for instance, it will block access to a newspaper like The Sun, it wouldn’t block that - but it would block pornography.”

Mr Cameron said he did not “believe” written pornography, such as erotic novel Fifty Shades of Grey, would be blocked under the plans. But he added: “It will depend on how the filters work.”

He also admitted it could lead to some interesting conversations in families. Asked if the “opt in” system meant a husband would have to “fess up” to his partner if he wanted to look at porn, he finally said: “Yes, it does.”

He then added: “I’m not saying we’ve thought of everything and there will be many problems down the line as we deal with this, but we’re trying to crunch through these problems and work out what you can do and can’t do.”

But others were critical of such a “nanny state” intervention. Daniel Foster, founder of web hosting company 34SP, said: “To say that pornography is ‘corroding childhood’ is extreme. Having criticised the previous government for operating a nanny state, this reeks of hypocrisy.

“The fact that there is plenty of widely-adopted filtering software readily available means that internet users are already acting autonomously in policing content in their own homes.”

Mr Cameron was even attacked by one of his former female MPs, Louise Mensch, for attempting to ban video containing rape simulation. She suggested such fantasies were common in more than half of all women. “It is not for our government to police consensual simulation, between adults, of one of women’s most common fantasies,” she wrote on Twitter.

Padraig Reidy, of the Index on Censorship, said people should not have to opt out of the filters. “If we have, as the Prime Minister is suggesting, an opt-out filter we have a kind of default censorship in place,” he said.

“Families should be able to choose if they want to opt in to censorship. If a filter is set up as a default then it can really restrict what people can see legitimately. Sites about sexual health, about sexuality and so on, will get caught up in the same filters as pornography. It will really restrict people’s experience on the web, including children’s.”

Dr Paul Bernal, from the University of East Anglia’s law school, suggested Mr Cameron’s crackdown on child abuse images was also inadequate. “Plans like these, worthy though they may appear, do not, to me, seem likely to be in any way effective,” he said.

“The real ‘bad guys’ will find ways around them, the material will still exist, will keep being created, and we’ll pretend to have solved the problem – and at the same time put in a structure to allow censorship, create a deeply vulnerable database of ‘untrustworthy people’, and potentially alienate many of the most important companies on the internet. I’m not convinced it’s a good idea.”

Filtering porn: problems with the plan

Can the filters work effectively?

Filtering pornography is fiendishly difficult to do accurately. Although the technology is improving, filters set up in hospitals several years ago had to be switched off after doctors were unable to access clinical studies on breast cancer.

Even if they do work, can they be circumvented?

Some schools have used web filters to stop children accessing Facebook when they were meant to be working. But some children reportedly got around them by using “proxy websites” that re-diverted them to Facebook around the filters. Such problems could also exist for pornography – while parents think there are safeguards in place.

What is pornography?

Some women’s groups believe that Page 3 in The Sun is pornography – not a view David Cameron shares. Computer algorithms may not be the best means of deciding what is and what is not pornographic.

Do we want to live in a nanny state?

The basis of Mr Cameron’s argument is that people should have to make a conscious decision to watch pornography. But civil liberties groups take the opposite approach and accuse him of hypocrisy. It was Mr Cameron who used to decry Labour’s nanny state.

And what about marital harmony?

Some men (and women) in happy relationships may secretly watch pornography without their partner’s knowledge. This, as Mr Cameron admits, will force them to fess up or abstain. A husband whose wife finds he has secretly turned off the porn filter could find himself in trouble – possibly straining the institution Mr Cameron cares most about: marriage.