Hannah Weller said she wanted other parents to join her and "take a stand for all our children".
Speaking outside London's High Court where earlier this year the family won £10,000 in privacy damages, she said: "We're calling for a change in the law to give children better protection from the prying eyes of the press. It should be a criminal offence to violate any child's right to grow up free from media intrusion."
Her husband, the 55-year-old former frontman of The Jam and The Style Council, sued Associated Newspapers for misuse of private information on behalf of daughter Dylan, who was 16 when the seven unpixellated pictures appeared on MailOnline in October 2012, and twin sons John-Paul and Bowie, who were 10 months old.
The pictures were published after a paparazzo followed Weller and his children on a shopping trip through the streets of Santa Monica, California, taking photos without their consent despite being asked to stop.
Hannah Weller said: "I am here today because we as parents decided to make a stand against this threatening, aggressive and abusive behaviour and when we did, the judge agreed with us that publishing photographs of children without parental consent is against the law. Thanks to our legal team, newspaper editors will think twice before publishing photographs of our children in the future.
"The law is now clear but sadly, it is not properly enforced. Many newspaper publishers continue to compromise the safety and privacy of children.
"As it stands, the decision about whether or not to thrust children into the media spotlight lies with the discretion of the editors of money-hungry newspapers and online gossip websites who are often more concerned with their own bottom line than the best interests of children.
"These people have shown repeatedly that they cannot be trusted to make the right choices and so it is time to take this decision from them and make it a criminal offence to expose children in this way. Children deserve special protection from the prying eyes of the press."