Of these more than 1,200 were either charged with a criminal offence, fined, cautioned or subjected to a verbal warning for bullying on social media sites such as Twitter, Facebook and Snapchat.
The figures were compiled by Sky News under freedom of information laws.
Every force in the UK was asked how many investigations they have launched in the last three years under Section 127 of the 2003 Communications Act, the law used to pursue those suspected of abuse on websites, social media and blogs.
According to responses from 34 police forces in the year 2011/12, 6,919 people were investigated, including 744 children. In 2012/13 6,974 cases were probed, including 578 under 18s.
In the first nine months of 2013/14, 7,318 people had been the subject of a police probe, of whom 610 were children.
Four 10-year-olds and one nine-year-old in Tayside, now part of Police Scotland, were given warnings by police, while 11,292 adults had some sort of formal police action taken against them.
Luke Roberts of charity BeatBullying, said. "In terms of social networking, we'd like to see more transparency, in terms of giving clear reporting mechanisms to children using those sites.
"But also importantly clear action, so that if a young person has the confidence to report something, they also know they're going to receive a message, or action will be taken."
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