The survey comes a year after the report by Mothers' Union chief executive Reg Bailey, entitled Letting Children Be Children, which called on businesses and broadcasters to play their part in protecting young people from the "increasingly sexualised wallpaper surrounding them".
The CIM is calling on the Government to work directly with the marketing industry to "deal with these pressing issues once and for all".
David Thorp, director of CIM research, said:
"It's clear that parents still have very real concerns about the way some companies try to sell to children. The marketing profession needs to address these concerns but we also want a dialogue between parents, the Government and industry bodies to ensure that our solutions are lasting and effective.
More top news
Young cancer patient Bradley Lowery stole hearts while on the Wembley pitch with the England squad.
A 30-year-old man has been arrested in Birmingham by officers investigating the Westminster terror attack, the Metropolitan Police said.
US airline United faces outrage after apparently ordering women to change or lose their seats for being not "properly clothed".