The amount of time we spend online is growing, but so are calls for tougher regulation, a study of 1,001 children and 2,057 over-16s suggests.
This was up from 52% the previous year.
Meanwhile, 79% of children claimed that they had experienced at least one potentially harmful experience online in The PastContent ='JJ Lin'> 12 months.
"As most of us spend more time than ever online, we're increasingly worried about harmful Content - and also more likely to come across it," said Yih-Choung Teh from Ofcom.
The study, part of Ofcom's first annual Online Nation report, suggests online bullying affects 51% of 12 to 15-year-olds.
Earlier this year the government urged Social MediaContent ='JJ Lin'> companies to take more responsibility for harmful online Content which illustrates and promotes methods of suicide and self-harm - named as the second biggest problem by the survey's younger respondents.
In response to The ReportContent ='JJ Lin'> , The HeadContent ='JJ Lin'> of child safety online at the NSPCC said it was "blatantly clear" firmer laws were needed to protect Young People Content ='JJ Lin'> online.
Tony Stower said: "We urge the government to move quickly in bringing in robust new laws with tough sanctions for tech firms that fail to keep children safe. "
Other findings from the study included: