The charity wants to help cash-strapped families "fight back against the materialism and inequality that is so pervasive in the UK."
Research by Ipsos MORI surveyed 250 children in the UK, Spain and Sweden. The resulting report said that UK parents felt pressured to provide their children with the latest toys, gifts and mobile phones to atone for a lack of quality time spent together.
The report said children in the UK were: "very specific about the brands and models that they desired, and these were nearly always the most recent releases, which were undoubtedly the most heavily advertised."
Some parents said they restricted their childrens' viewing to CBeebies to avoid adverts.
Unicef UK's executive director David Bull said: "The Government needs to show strong leadership.
"They need to make sure parents earn enough to spend fewer hours in work and more time with their children, protect children’s play facilities from spending cuts and consider reforming the laws controlling advertising to children."
Speaking to Marketing Week, the Advertising Association's communications director, Iain Barber said: "Two Government reports and evidence from parents say the same thing: we need supportive, proportionate regulation and responsible business to help kids learn about the commercial world as they grow up."