The call, which has been framed under the banner of the charity's three-year-old 'Food4Thought' campaign, comes hot on the heels of a suggestion by Prime Minister Gordon Brown that existing voluntary codes on non-broadcast advertising should be strengthened.
However, BHF is proposing a more draconian set of rules through enforced government regulation of marketing activity from TV to online, mobile, in-store promotions, sponsorship and outdoor posters.
The charity argues that the current Committee of Advertising Practice Code was not developed with the purpose of promoting health and as such is flawed.
It also points out that the code does not cover non-broadcast marketing techniques, which it claims are being increasingly used to circumnavigate broadcast advertising rules.
The BHF has drawn up a new regulatory system based on the idea that "individuals and organisations must not act in a way where the purpose or effect is to promote an unhealthy food product to individuals under the age of 16".
It goes on to suggest four guiding principles including the establishment of a new body independent of the advertising industry to monitor and enforce the new system.
The BHF is lobbying politicians and campaigners as well as urging support for MP Nigel Griffiths' Food Products (Marketing to Children) Private Members Bill.
According to the BHF, at least a third of children are currently overweight or obese, while British children spend an average of £13m on snacks and sweets each week.
The charity also claims that one in eight children have played a game on a food company website.
The call is at odds with a recent survey by the Advertising Standards Authority, which claimed that new rules governing the advertising of food and soft drinks are being observed almost to the letter.
The survey looked at almost 800 ads and found that without exception, advertisers were complying with the new rules that were adopted in the advertising codes in July last year.
The rules have been introduced amid concerns about childhood obesity, with the intention of restricting demand for less healthy foods, while encouraging the promotion of healthier alternatives.