Adverts for unhealthy food targeted at children could be banned across all media as part of efforts to tackle the obesity epidemic.
The Committee of Advertising Practice (CAP) has launched a public consultation on proposals to limit the placement of ads for products high in fat, salt or sugar (HFSS) in non-broadcast media, including traditional and online outlets.
It will also consider a ban on such ads targeting children as old as 16 to bring them into line with television regulations.
A ban on using celebrities or popular characters could also be partially lifted for the advertising of healthier foods.
Currently, HFSS food and drink can be advertised to children in non-broadcast media, unlike television where strict regulation prohibits it through content and scheduling restrictions.
On television, ads for HFSS food and drink cannot appear around programmes made for or likely to appeal to children up to the age of 16, and they are banned from screening on dedicated children's channels.
CAP, which sets the rules for UK advertising, said the move was in response to widespread concern about childhood obesity as well as the need to ensure rules reflected changing media habits among young people.
Evidence showed advertising had a "modest" effect on children's food preferences, with factors such as parental influence, opportunities for physical exercise and education playing a greater role in solutions to childhood obesity, CAP said.
However, it believed even a relatively small positive impact from new advertising restrictions could make a "meaningful contribution to tackling this important health issue".
The growth in popularity of the internet had changed the way children interacted with the commercial world, with Ofcom research showing that 96% of 12 to 15-year-olds spent more time online than watching TV last year.
A third of children are overweight or obese, and are in turn more likely to become obese adults and have a higher risk of morbidity, disability and premature mortality.
CAP chairman James Best said: "Too many children in the UK are growing up overweight or even obese, potentially damaging their health in later life and imposing a high cost on society.
"Advertising is just one small factor in a very complex equation but we believe we can play a positive part in addressing an urgent societal challenge.
"In proposing new rules, our aim is to strike the right balance between protecting children and enabling businesses to continue advertising their products responsibly."
The consultation closes on July 22.
Alex Neill, director of policy and campaigns at Which?, said: "A fundamental review of the rules governing how foods high in sugar, fat and salt are marketed to children up to 16 years of age is long overdue.
"New rules to cover how unhealthy products are marketed to children on social media and packaging, in line with TV advertising, will be vital to tackling childhood obesity."
Children's Food Campaign co-ordinator Malcolm Clark said: "We have long been calling for tougher restrictions on the marketing of less healthy food and drink to children on TV, online and beyond. We are pleased that CAP finally seems to have accepted the need to take action and to harmonise the rules across all forms of media, using the current restrictions on TV advertising as a starting point.
"However, the CAP consultation is a let-down compared to the brave and bold action we saw earlier this year with the Government's announcement of a sugary drinks levy. CAP has missed obvious opportunities to make the UK a world leader in putting the protection of children's health above food and advertising industry profits.
"There are too many gaps in the detail of the consultation and scope for the rules to be weakened and exemptions given to industry for us yet to have confidence that the end result will be the necessary leap forward that CAP and industry claim, or that parents and public health advocates want to see."