The figure has been come from Freedom of Information requests which were sent to police services in England and Wales by the NSPCC.
It is feared the true figure will be even higher, as only 34 police services supplied their data.
The NSPCC says technology and easy access to sexual material is “warping” young people’s views of what is normal behaviour.
The offences were all reported between 2009 and 2012 and the figures show that
98 per cent of the offenders were male and in more than three out of five cases the victims knew their abuser.
Claire Lilley, policy advisor at the NSPCC, said: “We hope our findings will ring alarm bells with the authorities that this is a problem which needs urgent attention.
“In some cases older children are attacking younger ones and in other cases it’s sexual violence within a teenage relationship.
“While more research needs to be done on this problem, we know that technology and easy access to sexual material is warping young people’s views of what is ‘normal’ or acceptable behaviour.”
She added: “We are treating an increasing number of children who have carried out online grooming, harassment in chatrooms and ‘sexting’.
“Children who are sexually abusive have often been victims of abuse, harm and trauma themselves. Exposure to this can make them think abusing someone or being sexually violent is okay.”
Last month, the Inspectorate of Probation published an inspection report on multi-agency responses to children and young people who sexually offend.
It states: “A sizeable number of them had been referred on previous occasions to children’s social care services but the significance of their sexual behaviour was either not recognised or dismissed. This, to us, represented a lost opportunity, both for the children and young people themselves and their potential victims.”
Any adult worried about a child or in need of advice can contact the NSPCC’s helpline on 0808 800 5000. Children can contact ChildLine on 0800 1111.