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Sir Cliff Richard has called for a “re-balancing of the legal system” as he launched a petition calling for anonymity for sexual offence suspects before they are charged.
Police raided Sir Cliff’s home in 2014 during an investigation into a sexual assault claim. He was never arrested.
The star said the media coverage of the raid left his reputation “in tatters”.
But the group Rape Crisis said false allegations were rare and there were “no grounds” to change the law.
Currently, alleged victims of sexual offences receive lifelong anonymity under UK law but there is no law against naming a suspect.
The College of Policing guidelines advise officers not to name those arrested or suspected of any crime “save in exceptional circumstances where there is a legitimate policing purpose to do so”.
Once a person is charged, they are routinely named by police.
Sir Cliff is one of several well-known figures backing the campaign group Falsely Accused Individuals for Reform (Fair).
The group’s parliamentary petition calls for those suspected of sexual offences to be given anonymity until they are charged unless there are exceptional circumstances.
It needs 100,000 signatures to be considered for a debate in Parliament and had attracted more than 3,000 signatures by the time it was officially launched in Westminster on Monday.
Speaking to reporters at the launch event in Victoria Tower Gardens, alongside BBC radio DJ Paul Gambaccini, Sir Cliff said: “We have both been through the mill. When you know you didn’t do it, you feel you’re in a hole you can’t get out of.”
He said: “People can be evil enough to tell a lie about an innocent person,” adding that “no smoke without fire” was a “stupid saying”.
Sir Cliff successfully sued the BBC for breach of privacy over its coverage of the police raid on his house, which it filmed from a helicopter.
At the campaign launch
By BBC News reporter Becky Morton
Both Cliff Richard and Paul Gambaccini spoke passionately about the impact being named in the press had on themselves and their families.
Richard described how he struggled to sleep and felt like he “had been hung out to dry”
“You can’t forget it,” he said. “No one knows what you go through unless you have gone through it.”
However, both made clear the campaign was not only about themselves but also the hundreds of others still experiencing what Mr Gambaccini described as “torment”.
The growing crowd which watched their speeches was broadly supportive and included a handful of Cliff Richard fans who were in London to watch the singer’s concert that evening.
However, they faced tough questioning about whether the change would hinder other genuine victims coming forward, against a background of low rape convictions.
Sir Cliff insisted that if someone was charged they could be named and other potential victims would still have months to go to the police before a trial.
The change was a “compromise”, he argued, that would help “readjust balance” he said was currently stacked against the accused.
Earlier on Monday Mr Gambaccini warned of a “false allegation crisis”.
The BBC DJ was arrested over sexual abuse allegations in 2013 in the wake of the Jimmy Savile scandal but the case was dropped a year later.
Mr Gambaccini told Radio 4’s Today programme that having his identity revealed made the year he spent on bail on suspicion of sexually assaulting two teenage boys more difficult, leaving him living “under a cloud of suspicion”.
Asked whether publicly naming suspects after they have been arrested encouraged more victims to come forward, Mr Gambaccini said: “This is not a competition, who has been hurt the most.
“There are actually two crises – one is a sex abuse crisis and the other is a false allegation crisis. When you solicit more accusations, most of them turn out to be false.”
Mr Gambaccini said under the changes the group wants – which would give suspects anonymity until they are charged with an offence – further victims would be able to report their abuse when the person was charged.
Charity Rape Crisis said false allegations of rape, sexual abuse and other sexual offences were rare but had “disproportionate media focus on them”.
“The subsequent widespread myth that they are common contributes to an environment in which it’s very difficult for victims and survivors to talk about what’s happened to them and seek the support and justice they want, need and deserve,” said Katie Russell, national spokesperson for Rape Crisis England and Wales.
She added: “Giving these suspects exceptional treatment compared to those suspected of similarly serious and stigmatising crimes would inevitably reinforce the public misconception – which is unsupported by evidence but nonetheless widely held – that those suspected of sexual offences are more likely to have been falsely accused than those suspected of other types of crime.”
Both defendants and complainants in rape cases were granted anonymity in 1976, but Parliament repealed anonymity for defendants 12 years later.
It was argued that comparison should be made not between a rape defendant and alleged victim, but between a rape defendant and a defendant charged with another serious crime.
Anonymity has since been extended to those alleged to be victims of other sexual offences, not just rape.
