The Growing Up Digital report said the explosion in children's social media use means typical three to four-year-olds spend eight hours, 18 minutes a week online.
And 12 to 15-year-olds use the net for at least 20 hours a week.
Rules buried in social media sites' terms and conditions allow youngsters' pictures and messages to be bought and sold by the web giants, who can target them for advertising without their knowledge.
Instagram's terms and conditions say users have to be at least 13. But of a group of teenagers asked to read them, not one fully understood what they were committing themselves to.
The report recommended the site warn young users: 'We may keep, use and share your personal information with companies connected with Instagram. This information includes your name, email address, school, where you live, pictures, phone number, your likes and dislikes, where you go, who your friends are, how often you use Instagram.'
It comes amid concern over children's growing addiction to sites such as Facebook and Twitter and the lack of control they have over the photos and messages they post.
The report called for sweeping regulation of social media and compulsory online education from the age of four to ensure children are not 'overwhelmed'.
Produced by a group including a libel lawyer, a BBC children's director, charity chiefs and a London School of Economics academic, the report called for more regulation to protect youngsters' privacy.
It added: 'Although much of the behaviour children complain about online - bullying, sexting, harassment - is illegal, a number of studies have found that children often do not know how to report concerns and, when they do, are dissatisfied with any action taken.'
The report said this was 'particularly troubling in online bullying cases where the record of abuse is public and permanent.'
Six out of 10 children who are bullied receive the abuse online, the report said. But of these, only 15 per cent reported it to the relevant social media site.
The report said a digital ombudsman should be set up to mediate between such sites and young people over removing content.
Longfield said: 'Children spend half their leisure time online.'
'The internet is an incredible force for good but it is wholly irresponsible to let them roam in a world for which they are ill-prepared, which is subject to limited regulation and which is controlled by a small number of powerful organisations.'
Children's charities welcomed the report. A spokesman for the NSPCC said: 'We have long called for greater openness by internet companies about what they are doing to keep children safe and what action is taken to remove content when concerns are raised.'
Barnardo's chief executive Javed Khan said: 'This report provides further worrying evidence of how children are unprepared to deal with life online.'
Instagram did not respond to requests for comment.
