The NSPCC poll conducted by YouGov found that while most of the 2072 Britons questioned supported historic abuse cases being prosecuted, 31% said alleged victims of sexual offences had little chance of getting justice.
It revealed 81% of those asked supported old cases being pursued, 65% backed Operation Yewtree; the investigation launched in the wake of abuse claims against Jimmy Savile.
Only 39%, however, thought alleged victims of sex crimes had a fair chance of justice.
Peter Watt from the NSPCC said: "Whilst it's reassuring that the public strongly support prosecuting cases of child sexual abuse, even where they go back many years, they understand there are difficulties in doing this.
Less than half of the public think victims have a fair chance of getting justice and this reflects the fact that the conviction rates are still lower than for other crimes.
"But we are starting to see a system wide shift in how these cases are approached by the police and [England's] Crown Prosecution Service .
"We now need to push these reforms all the way through the process to the courts as well. Simple changes like video evidence and advocates for young or vulnerable."