The British Heart Foundation (BHF) wants to lead the way in banning online junk food advertising that targets children.
The BHF report "Protecting Children" shows two thirds of parents are not aware that junk food manufacturers use internet games to target children.
They support proposed regulations that will cover all forms of marketing online including food and drink packaging.
The Food Products (Marketing to Children) bill plugging a ban on online junk food adverts introduced by MP Nigel Griffths is due to be debated in parliament this April.
BHF Director of Policy and Communications Betty McBride said: "Junk food manufacturers are laying a multi-million pound honey trap for children. They are luring kids into their online playgrounds or stalking them on food packaging at the breakfast table.
"These regulations are a vital prerequisite to enable any government strategy on childhood obesity to be effective. They have the potential to transform the supermarket experience for stressed parents and change the way future generations of children view food."
Children's Food Campaign Coordinator Richard Watts, who authored the report, said: "The current system of self-regulation is clearly not fit for purpose in the twenty-first century. It is designed to prevent dishonest claims, not to improve children's health.
"Properly enforced statutory rules are the only way to protect our children from junk food marketing."