Three quarters of police forces in England and Wales responded to a Freedom of Information request by the charity. A total of 5,028 such offences have been reported since 2009. In some cases, the accused was as young as five or six. Allegations included rape and serious sexual assaults.
Almost all of those accused (98 per cent) were boys and in three out of five reports the alleged perpetrator knew the victim. A family friend was named as an abuser in one in three cases and a family member was accused in one in five reports.
The NSPCC said that the police, social workers and teachers need to get better at spotting warning signs of sexual abuse. Specialist treatment for abusers also needs to be more readily available.
The charity also cited easy access to online pornography and other indecent material as a factor in the high number of young people who sexually abuse.
Claire Lilley, NSPCC policy adviser, 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 that the charity has noticed an increase in the number of children it supports that have been involved in online grooming 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,” Lilley said.
Last month, a Probation Inspectorate report looking at 24 cases of children who sexually abused found court delays left “lengthy periods” where they were offered no help to address their behaviour. It also found that examples of joint support across justice, health, education and social care were rare.