A ban on all junk food marketing aimed at children, including online games, is being called for by campaigners.
The British Heart Foundation (BHF) and the Children's Food Campaign are calling for the rules on packaging and online marketing to be tightened.
A ban on adverts for junk food during television programmes aimed at children under 16 is already in force.
The government said time was needed to assess the impact of the existing law before extending it.
A BHF survey found many parents were unaware some food firms had online games aimed at children and more than half did not realise that games and quizzes appeared on food and drink labels.
Regulation 'limited'
The survey questioned 1,069 parents of children aged seven to 14 years in November.
It found only 30% were aware that some junk food firms used online games to attract children.
And 52% of parents did not realise that games and quizzes appeared on food and drink labels.
The BHF and the Children's Food Campaign want the existing regulations extended to cover all forms of marketing aimed at children.
"Restrictions on advertising are just one part of a much broader set of actions government is taking"
They are calling for packaging, internet sites, product placement and sponsorship all to be included in marketing regulations.
They say the current regulation is limited and allows some forms of marketing to slip through the net.
The ban on adverts for junk food during television programmes came into force at the beginning of the year.
Regulator Ofcom outlawed adverts for foods high in fat, salt and sugar in an effort to tackle rising childhood obesity levels.
BHF director of policy and communications Betty McBride accused junk food manufacturers of luring children to online playgrounds.
Commenting on the proposed changes to marketing rules, she said: "They have the potential to transform the supermarket experience for stressed parents and change the way future generations of children view food."
A Department for Culture, Media and Sport spokesman said it was committed to tackling childhood obesity and had "significantly" tightened the rules last year.
"We must have a proper opportunity to assess the impact of these new rules, which are amongst the toughest in the world, before considering further restrictions," he said.
"Restrictions on advertising are just one part of a much broader set of actions government is taking to support the public health agenda."
The Food and Drink Federation has described the calls for further restrictions as "not based on reality".
"When it comes to marketing, the UK already has some of the strictest rules in Europe - thanks to a combination of regulation and voluntary action covering TV and non-broadcast marketing. These rules are dramatically changing the marketing landscape in this country. "
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