Our disbelief is the sexual predator's great asset

The problem was not tolerance of abuse but disbelief of anyone who dared complain

Joan Smith: 'Until Hall suddenly changed his plea to guilty, he lied through his teeth about his assaults on girls' (PA)

If the broadcaster Stuart Hall ever felt a scintilla of anxiety that one of his victims might report him, I doubt whether it troubled him for long. Confident predators like Hall know that almost everything the public believes about sexual violence is wrong, and they take full advantage of the fact.

People are wrong about the kind of men who commit sexual assaults; they're wrong about how victims behave after they've been attacked; and they're hopelessly bad at deciding who is telling lies.

Until Hall suddenly changed his plea to guilty, a fact that couldn't be reported until last week, he lied through his teeth about his assaults on girls in the 1970s and 80s. It emerged on Thursday that he had pleaded guilty at an earlier hearing to 14 charges of indecent assault, allegations which he had publicly denounced as "pernicious, callous, cruel and above all spurious". It is hardly a stretch of the imagination to picture Jimmy Savile reacting in similar terms if even a fraction of the allegations against him had become public knowledge in his lifetime.

The problem in those days was not tolerance towards sexual offences but disbelief of anyone who dared make a complaint, especially if the suspect was well-known. We know now some of Savile's victims came forward in his lifetime but he never had to face them in court. The emerging accusations about a string of sexual assaults in children's homes in north Wales tell a similar story. In each case, abuse appears to have been widespread, but victims had little confidence that their testimony would be believed.

What has changed is that police and prosecutors have finally begun to understand the damage done by popular myths about rape. Thanks to academic research and evidence from rape crisis centres, the balance of belief has shifted from massively favouring predators to listening to victims. But this crucial change has yet to be accepted by the public. Ordinary people still believe, wrongly, that rates of false accusation are higher for rape than for other offences.

What they're reacting to is decades of lurid and inaccurate headlines in papers like the Daily Mail, which loves to frame the central problem of rape as the risk to men of unjust accusation. The truth is that false accusations of both rape and domestic violence are "extremely rare", according to the Director of Public Prosecutions, Keir Starmer, who published detailed research this year.

It is far more common for genuine victims to decide against going to the police, in some cases for decades, because they're terrified of not being believed. They're also afraid of being humiliated and accused of lying in court, an experience which the violinist Frances Andrade found so devastating that she took her own life during the trial of her abuser. Yet the public is so fixated on "false" allegations that a new survey shows that three-quarters believe rape suspects should be given anonymity until convicted.

It is hard to think of a proposal more likely to ensure that sexual predators go free. Prosecutions for rape or sexual assault are much more likely to succeed when jurors can be shown a pattern of offences, instead of having to make their minds up about the testimony of just one or two witnesses. Most of Hall's victims came forward only when they saw the publicity around his initial arrest, helping Lancashire police to build a rock-solid case against him.

Other rape myths need to be demolished, including the notion that victims bring it on themselves. The reality is that rapists pick victims they see as vulnerable, such as the five-year-old girl who died of her injuries in India last week.

The notion that there's something peculiarly stigmatising about allegations involving sex crimes is equally nonsensical, as anyone who has been accused of child cruelty can attest. But there is also a fundamental public misunderstanding about the nature of sex offenders, most of whom are far from the stereotype of the "frustrated" individual who commits an uncharacteristic single offence. Rape is much more common than murder and it makes more sense to worry about serial rapists than serial killers. Savile is an extreme case but not the only one: John Worboys, the "black cab" rapist jailed in 2009, is believed to have drugged and raped more than 100 women across London.

The cunning of such men obscures the extent of their offending and discourages victims from coming forward; it is only when someone is arrested and survivors realise they aren't alone they feel able to go to the police. It could not be clearer that Hall would have gone on proclaiming his innocence, and wallowing in self-pity for the cameras, had the number of his accusers not become too large to dismiss.

As the extent of "historic" sex abuse becomes shockingly evident, misplaced public sympathy for men accused of such offences risks putting justice in jeopardy again. A country where a well-known man has only just been called to account at the age of 83 can hardly be accused of being too tough on sexual predators.

Joan Smith is Political Blonde: politicalblonde.com; twitter.com/@polblonde