Deedaa yes, it is difficult to prove beyond doubt that abuse has taken place historically. It often hinges on the memory of the complainant, who is able to describe intimate physical details of the alleged abuser and/or the environment in which the abuse took place, that they would otherwise have no way of knowing. Offenders deny abuse on different levels, from claiming that they weren't even on the same planet at that time, to saying that they might have touched the victim, but were too drunk to remember. Partial admissions, independent corroboration of the same behaviour from other victims, school, medical and police records of complaints not acted on, and many other sources of evidence that, on their own are insufficient, all add up during the trial, which would not stand much chance of taking place without the CPS thinking there is sufficient evidence to proceed. Then it's up to the jury to decide whether it's been proved beyond reasonable doubt.
Many sex offenders eventually talk more honestly about their trials during group treatment. Not only did they lie and deny to try to escape conviction, they claimed their victim was insane, hysterical, deluded, mistaken, actually consented - anything rather than take responsibility and acknowledge that their behaviour had caused many years of distress. Vehement denial takes many forms and detectives, psychiatrists and sex offender treatment facilitators have learned how to interview sex abusers and identify the discrepancies in their accounts. If the CPS do prosecute Rolf Harris and others, there needs to be some evidence to begin with that needs close examination. Charges will be dropped if there isn't.