GCHQ will be brought in to tackle the problem of child abuse material being shared on peer-to-peer networks, the prime minister has revealed.

Following the announcement that Google and Microsoft are to step up efforts to remove links to child abuse material from search results, Cameron has turned his attention to less conspicuous methods of sharing illicit data.

Talking to the BBC's Jeremy Vine, Cameron argued that the "dark net", a general term for areas of the internet not accessible through search engines, was policeable.

"There's been a lot in the news recently about the techniques, ability and brilliance of the people involved in the intelligence community, in GCHQ and the NSA in America. That expertise is going to be brought to bear to go after these revolting people sharing these images [of child abuse] on the dark net, and making them available more widely," the prime minster said.

"You use technology which is able to get into the dark internet, that is able to decrypt encrypted files, and that is able to find out what is going on. Like all these things if you put in the resources and the effort, if you use the best brains – the brains that are, as it were, the inheritors to the people that decrypted the Enigma code in the second world war – if you take those brains, and apply it to the problem of tackling child abuse online, you'll get results.

"I'm confident, having sat in the cabinet room, listening to the internet service providers, and having listened to the national crime agency, having talked to the team that are going to be negotiating with the Americans to work out how we best bring our joint expertise to bear on this, I'm confident that we can make some real progress."

Asked whether people would be comfortable with the invasion of privacy that would result from the move, Cameron responded that "people understand that a crime is a crime whether it's committed on the street or the internet".

• The four biggest UK ISPs will start making existing users decide whether to filter adult images