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.
The average British adult spent three-and-a-quarter hours a day online last year, said the study by Ofcom and the Information Commissioner's Office.
But while most people say the internet makes their lives better, 70% of adults said they would like tighter rules for sites such as Facebook and Instagram.
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 past 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.
However, Mr Teh said for most people those risks are still outweighed by the internet's benefits.
"People... recognise the importance of protecting free speech - which is one of the internet's great strengths," he added.
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 media 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 February, Instagram said it would remove all graphic images of self-harm after the father of 14-year-old Molly Russell, who took her own life in 2017, said Instagram had "helped kill" his daughter.
In response to the report, the head of child safety online at the NSPCC said it was "blatantly clear" firmer laws were needed to protect young people 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:
- The amount of time we spend online is growing by about 7% each year
- The most potential harmful content children said they saw online was on Facebook (24%), followed by Instagram (12%) and Snapchat (8%)
- Spam emails were the most prolific harmful content cited by adults (34%) followed by fake news (25%) and scams (22%)