More children were counselled by ChildLine for sexual abuse last year than ever before, the service said today.
A total of 13,237 children called the helpline in 2007/08 saying they were victims of sexual abuse - more than a 50 per cent increase over three years.
The figures showed that more than 36 children, including one aged under seven, called the helpline every day last year saying they were victims of sexual abuse.
ChildLine said that, despite having more volunteers and bases than ever, it was only able to answer two-thirds of the 2.3 million calls it receives every year.
Esther Rantzen, the service's founder and president, said: "There are many children whose cries for help cannot be answered because ChildLine simply does not have enough resources to answer every call.
"Our nightmare is the child who plucks up the courage to ring, fails to get through, and never dares try again. Imagine the distress of a child who cannot get through to a counsellor before she is raped again that night."
She said the service urgently needed to be expanded "so that every child's cry for help can be answered".
Sue Minto, head of ChildLine, said many child sex abuse victims had been "threatened or intimidated into silence" and some calls included "details of other extreme forms of abuse like being hit, tied up, threatened with their life and being plied with drugs".
She added that awareness campaigns and child sex abuse storylines on TV programmes like BBC soap EastEnders encouraged children to speak out.
"More children now understand what sexual abuse is and are increasingly willing to turn to ChildLine for help," she said.
The service counselled 13,237 children, including 465 children aged seven or under, for sexual abuse last year, more than at any time in its 22-year history. Almost 6,000 children said they had been raped.
The figure was up from 8,637 in 2004/05 - a 53 per cent increase over three years. During the same period, the overall number of children counselled rose 26 per cent.
Most children counselled for sexual abuse - 61 per cent (6,681) - were aged 12 to 15.
Of the 13,237 children counselled for sexual abuse in 2007/08, the vast majority were abused by someone they knew.
ChildLine said 59 per cent said they had been sexually abused by a family member, 29 per cent said they had been sexually abused by someone else known to them and 4 per cent said they had been sexually abused by a stranger.
A total of 8,457 were girls (64 per cent) and 4,780 were boys (36 per cent).
The NSPCC, which provides ChildLine, appealed for the public to donate to its three-year £50m Child's Voice Appeal, which was launched last year.