David Cameron has said he would never support a ban on topless images on page 3 of the Sun newspaper, as he set out plans for greater regulation of online pornography.

Pressed to explain the distinction between his proactive position on online pornographic images and his laissez-faire stance on topless images in newspapers, he said that it was up to consumers whether or not they wanted to buy the Sun.

"This is an area where we should leave it to consumers to decide, rather than to regulators," he said in an interview on BBC Radio 4's Woman's Hour.

Campaigners backing the No More Page 3 petition, which has been signed by more than 100,000 people since last summer, argue that the issue does not come down to consumer choice, because so many people are exposed to the images in the Sun inadvertently, confronted by it in cafes, in the workplace and on public transport.

"We have to always ask the question where should we regulate and where shouldn't we regulate, and I think on this one I think it is probably better to leave it to the consumer," Cameron said. "In the end it's an issue of personal choice whether people buy a newspaper or don't buy a newspaper."

Asked by Woman's Hour presenter Jane Garvey whether he was worried that his daughters could be confronted by Page 3, he repeated: "This is an area where we should leave it to consumers to decide, rather than to regulators … As politicians we have to decide where is the right place for regulation, where is the right place for legislation, where is the right place for consumers to decide."

The founder of the No More Page 3 campaign, Lucy Holmes, said she thought Cameron's willingness to acknowledge the dangers of online pornography while ignoring the parallel dangers of topless images on page 3 of Britain's best-read newspaper was "peculiar".

"The problem is that none of us get the choice of whether we want to live in a society where newspapers are primarily there for men's sexual pleasure. All we want to see is women represented with respect in the tabloid media, but everywhere we see female sexuality and the female body presented as being there for men," she said.

"David Cameron must see that these pictures are damaging for women. Is he afraid of upsetting the Sun?"

There are signs that the No More Page 3 campaign may be beginning to have an impact. In February, Rupert Murdoch responded to a Twitter user who described Page 3 as "so last century", replying: "You may be right, don't know but considering. Perhaps halfway house with glamorous fashionistas."

Newspaper reports this weekend suggest the Sun's new editor, David Dinsmore, has asked female executives to start thinking about "reinventing" Page 3 to update it.

The National Association of Head Teachers has signed the petition amid concerns that children can find such images "confusing and embarrassing". The Girl Guides association has also signed it.

Caroline Lucas, Brighton's Green MP, recently asked Cameron during prime minister's question time whether he would support a request to get parliamentary authorities to stop the Sun being available on the parliamentary estate.

"The government's own research shows that there is a link between the portrayal of women as sex objects in the media and greater acceptance of sexual harassment and violence against women. That being the case, will the prime minister join me in trying to get our own House in order and calling on the parliamentary authorities to stop the Sun being available on the parliamentary estate until Page 3 is scrapped, and will he have a word with his friend Rupert Murdoch about it while he is at it?" she asked.

Cameron replied: "I am afraid I do not agree with her. It is important that we can read all newspapers on the parliamentary estate, including the Sun."

The No More Page 3 campaign was launched last summer during the Olympics by Holmes, who was infuriated to find that the biggest image of a woman in the newspaper was not an athlete, but a young model wearing just her underpants, captioned "Emily from Warrington".