Parliament must "recognise extreme emotional abuse" and give child protection services greater power by legislating against it, a senior member of the NSPCC said.
John Cameron, head of child protection operations, said the so-called "cinderella law" was not about punishing parents who did not buy their children "the latest gadgets or trainers":
The Government has indicated they are set to outlaw extreme emotional cruelty and this is a positive step forward and the publicity around this and highly publicised cases such as Daniel Pelka may have contributed to the sharp increase in calls.
We must recognise extreme emotional abuse for what it is - a crime - and those who carry it out should be prosecuted.
This isn't about prosecuting parents who don't buy their children the latest gadgets or trainers, this is about parents who consistently deny their children love and affection.
Peter Watt, the NSPCC's director of national services, said:
The responses these victims received when they first revealed Savile's sickening crimes makes heart-rending reading.
They were ignored, dismissed, not believed, laughed at and, astonishingly, told in some cases they should feel lucky he had paid them attention.
Half a century on, the world finally discovered just how dreadful his crimes were - something these men and women had known all that time but felt powerless to do anything about.
The anger, frustration and sheer helplessness of the situation obviously damaged their lives in various ways.
But they showed true courage in coming forward once more to talk about their experiences and hopefully they can now start to put the terrible trauma behind them.
According to the report, Would They Actually Have Believed Me?, some of the victims, who were aged between eight and 26 when Savile assaulted them, told hospital staff, who dismissed their claims.
One of the 26 victims interviewed by NSPCC counsellors went to the police but no action was taken. The vast majority were children when they were abused but four were adults.
The NSPCC said the research, which was commissioned by Her Majesty's Inspectorate of Constabulary, highlighted the "devastating scars" that victims had suffered from the abuse, with some turning to drink and drugs to cope.
Others have suffered mental illness, poor relationships or contemplated suicide, it said.
Head of Child Protection Operations at the NSPCC, John Cameron, says children have a "greater likelihood" to be involved in criminal and anti-social behaviour if "they have been in receipt of smacking as a standard form of parenting".
Speaking with ITV News, Mr Cameron said smacking does not have a positive, long-term impact on children.
"This is not about prosecuting, persecuting and criminalising parents, but it's about giving a very strong message in our society that children should have the same rights as adults in law to be protected from physical assaults," he said.
The NSPCC has welcomed Google and Microsoft's decision to block images of child abuse via their search engines, but emphasised, "We must keep one step ahead."
Peter Wanless, chief executive of the children's charity, said:
Each image is a crime scene where unspeakable abuse was committed.
As sex offenders get ever more technologically advanced in pushing their vile trade, we must keep one step ahead and this requires a concerted and sustained effort from all quarters.
This is the key child protection issue of a generation - we cannot fail.
The NSPCC is calling for social media sites to do more to make their online platforms safer for the millions of children who use them by bypassing the age restrictions. Claire Lilley, NSPCC's head of child safety, said the risks to 11 and 12-year-olds need to be evaluated by the companies.
There is a significant jump in the numbers of children who have a social networking profile at age 11 - which coincides with the move to secondary school for most UK children
We estimate that around half of the UK's 11 and 12-year-olds have a profile on a social networking site with a minimum age of 13.
Age verification is a nut that social networking sites are yet to crack.
We want social networking sites like Facebook and Twitter to take a pragmatic approach - if younger children are determined to use social networking sites for over 13 year-olds, the sites can't simply turn a blind eye.
BeatBullying has backed calls from the NSPCC for social media sites to do more to protect their young users.
BeatBullying founder Emma-Jane Cross said:
"This research underlines the urgent need for social networking sites to take their young users' safety much more seriously.
"We believe in the right of children to go online without fear of being bullied or harassed, and this cannot be achieved until social networks put adequate resources behind safeguarding and user verification policies."
The NSPCC are calling for social media sites to acknowledge that many of their users are under the age of 18, in order to do more to safeguard their child users.
The comments come as new research by the children's charity found that around half of the UK's 11 and 12-year-old regularly use social media, and of these, a quarter said they had been upset by something on it.
A quarter of children aged between 11 and 12 who use social media have been upset by something on it over the past year, new research from the NSPCC has revealed.
A poll of more than 1,000 youngsters also found that a fifth of children who had been upset by an online incident such as trolling, bullying or being sent inappropriate sexual messages, experienced this every day or almost every day.
Justice Minister Damian Green admitted more work was needed to help children be supported through the court process. Responding to the NSPCC report that highlighted failures in adequate care of young and vulnerable witnesses at criminal proceedings, he said:
There are a range of measures available to help reduce the anxiety of attending court, including giving evidence behind a screen or the use of a registered intermediary, which has increased significantly over recent years. We are also trialling pre-recorded evidence for young and vulnerable witnesses.
We recognise that more work needs to be done.
I have ordered an investigation into how we might reduce the distress caused to victims from cross examination from multiple defence barristers without compromising the fundamental right to a fair trial.