There were 31,000 offences recorded in the year up to April 2014, up 8,500 on the previous year.
Figures compiled by the charity show 85 offences were recorded by police every day, with significant rises in Scotland and Northern Ireland also.
A spokesman said high-profile cases had “played a contributory factor” in encouraging people to come forward reports BBC.
Jon Brown, from the NSPCC’s sexual abuse programme, told BBC Radio 4’s Today that cases in Rotherham, Rochdale, Oxford and elsewhere had helped prompt “children, young people and adults to speak about abuse that is either happening to them or has happened to them”.
Chief Constable Simon Bailey, the National Police Chiefs Council (NPCC) lead for child protection, said police now looked “upon child abuse very differently”.
“Many, many, more” people had found the confidence to report incidents, he said, but the latest figures could be still only be the “the tip of the iceberg.”
And Peter Wanless, the NSPCC’s chief executive, said the figures were “a fraction of the true number of victims, because some endure an agonising wait of many years before telling anyone – and others never reveal what has happened to them”.