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
Rebecca Johnson, 25, was working as a tour guide with the Santa Safari team when she was killed.
Bahrain couldn't be more different to the UK right now.
Mrs May denied she was forced to "grub around" for deals as she said that the UK will raise human rights with Gulf leaders at summit.