Every time a celebrity is acquitted of rape allegations, a pernicious media campaign clamours for anonymity for defendants to stop women and children from wrecking vulnerable men's lives. Most recently, we saw this after the Michael Le Vell trial.

Women Against Rape (WAR) and Lisa Avalos began to work on collaborative research in 2012 to compare how women accused of lying are treated in the US and the UK. Despite different legal systems, the findings shine a light on the UK, with poor investigations being found to be the central obstacle to justice.

In both countries, false reports are extremely rare. The chief crown prosecutor for London, Alison Saunders, says that "studies have indicated that only 2% of all reported rapes are false, which is slightly less than false reporting in all other crimes". Their incidence is dwarfed by the prevalence of unpunished sexual violence. The International Association of Chiefs of Police (IACP) in the US claims that only 3% of all rapists serve prison terms for their crimes.

This is the context for the prosecution of women who report rape. This happened in three cases that the US research profiles. "Patty" (Wisconsin, 1997), Sara Reedy (Pennsylvania, 2004) and DM (Washington state, 2008) found themselves treated as suspects after reporting rape to the police. Each was prosecuted for false reporting – her name cleared only when her rapist was caught raping again.

When DM's rapist, Marc O'Leary, was caught, photos of his many victims – including DM – were found on his phone. He is now in prison for multiple rapes, at least three committed after DM reported. Reedy's rapist, Wilbur Brown, carried out at least two attacks after police didn't investigate Reedy's complaint. When caught, he confessed to raping Reedy, and is currently in prison for at least 11 sexual assaults. Patty's story is similar. DNA evidence conclusively linked convicted rapist Joseph Bong to her rape, but not until Patty's efforts to clear her name bankrupted her.

These cases show some of the tragic consequences of prosecuting those who report rape. Consider Jimmy Savile's victims, many of whom went to the police and had their complaints disregarded, enabling him to continue offending.

According to the IACP, the most significant barrier to successful investigations and prosecutions is "the powerful and pervasive myth that most sexual assault allegations are false". It has designed guidelines to ensure proper investigation. The guidelines require police to set aside myths about rape and to approach victims with empathy and an open mind. They instruct police not to become sceptical because of a victim's post-assault behaviour (such as inconsistencies which may reflect the trauma they suffered); not to pressure a victim to retract; and not to stop investigating a rape and shift their suspicions to the victim.

IACP guidelines were clearly not followed in the three cases above. In each, police decided early the woman had lied, disregarded physical evidence of the rape and investigated her rather than her rapist. They also put severe pressure on each woman to retract. DM and Patty did, and the police then used the retraction to charge them.

IACP guidelines also state that a report of sexual assault can only be considered false "if the evidence establishes that no crime was committed or attempted" and "only after a thorough investigation". If this one guideline had been followed, all three prosecutions would never have happened.

How many other rape victims were prosecuted because of incomplete police investigations? We haven't had such conclusive proof in the UK because the attackers of, for example, Gail Sherwood and Layla Ibrahim, imprisoned after reporting rape, have not been identified. But was sloppy or sexist police work an issue? Another UK woman was prosecuted for "false retraction" despite the police knowing the man was violent, and recently one teenager who came to WAR for help would have been prosecuted had she not persisted – new tests found semen where police claimed there was none; the rape prosecution was reopened.

There is no parallel clamour in the US for anonymity for men accused of rape. To single out rape defendants from defendants of other heinous crimes, including murder, would be considered unjustifiable – a key reason WAR has opposed it in the UK.

But the prosecution of women for alleged false reports strengthens the myth that women frequently lie about being raped and discourages victims from coming forward. It diverts law enforcement away from thoroughly investigating rape and lets rapists loose on the public. It is not in the public interest, and must be stopped.

This is even more urgent in the UK, where women are much more likely to be jailed than in the US: most US states consider false reporting a misdemeanor, while Sherwood was sentenced to two years, Ibrahim to three.