Three-quarters of parents are concerned that 3G mobile phones could put their children's safety at risk.
A poll by NOP found that 78 per cent of the 624 parents surveyed believed the new phones would make it "more or less impossible to supervise or support children who use the internet".
Phones available later this year will offer internet connectivity, built-in cameras and can carry video images, said children's charity NCH, which commissioned the survey.
NCH's internet advisor John Carr said in statement: "NCH believes this throws down a major challenge to the mobile phone operators. If they want these phones to take off in the youth market they are going to have to convince a lot of parents that they are safe, or can be made safe."
The survey also found that a third of parents believe their child knows more than they do about mobile technology, even though two-thirds said they are responsible for ensuring their children are properly educated about new mobile phone technology.
Only 14 per cent believed such education to be the responsibility of mobile phone companies, while 10 per cent said it was the government's responsibility.
NCH recommends that every child's handset is preinstalled with filtering or screening software set to a high level.
The charity added that until this is installed as default, internet access on mobile phones should be classified as an adult service, with under-18s automatically barred.
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