One in six 6-year-olds are routinely allowed online for up to an hour a day without parent supervision, a survey of 20,000 Internet users by British telephone and Internet firm TalkTalk found.

For 7-year-olds, the proportion was two in five. Across the 6-to-17-year-old age group, half of all Internet use occurs without adult supervision.

Fourteen percent of 6-to-10-year-olds view adult content on the Internet, either by accident or on purpose.

Many parents said they didn’t need to monitor their children’s Internet habits because their children only listen to music or visit social networking sites. Some had set up security measures or reviewed their children’s Web history.

TalkTalk’s commercial director Tristia Clarke said she was astonished that 54 percent of parents said they “don’t have the time or the inclination” to monitor their children’s Internet use.

The survey also found that richer families were slightly more likely to let their children go online unsupervised than poorer ones.

Meanwhile, a separate study by British communications regulator Ofcom has found that nearly half of teens own a smartphone—nearly twice the proportion of adults who do. Out of these teens, 60 percent say they are highly addicted to them. It would be difficult for parents to monitor what their teens access via their smartphone.

Modern technology creates new challenges for parents. But parents still have a vital role in protecting and guiding their children’s minds, even in their teenage years. For more information on this, see our article “Deprive Your Children.”