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 a change in the law so those suspected of sexual offences have anonymity until they are charged, unless there are exceptional circumstances.
It reached 10,000 signatures on Monday afternoon, which means the government will respond. It needs 100,000 signatures to be considered for a debate in Parliament.
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
The launch outside Parliament started surprisingly low-key, with the media initially outnumbering the rest of the audience - including a handful of Cliff Richard fans, in London for the singer's show that evening.
But there was a rumble of excitement as Sir Cliff arrived to make his speech.
Both he and Paul Gambaccini spoke passionately about the impact on themselves and their families of being named in the press
They also made clear the campaign was not only about themselves but also the hundreds of others going through what Gambaccini described as "torment".
The growing crowd that gathered to watch appeared broadly supportive, although there was a brief disturbance as a member of the public called for police to be held accountable for their actions in such cases.
There were also shouts of support from Sir Cliff's fans, who the singer thanked for continuing to stand by him. "My fans have more sense than I thought," he told the crowd.
The pair were equally passionate in their defence when questioned about whether the change could hinder other genuine victims coming forward, against a background of low rape convictions.
Sir Cliff insisted what they were calling for was a "compromise" that would help "readjust the balance" he argued was currently stacked against the accused.
The BBC's legal correspondent Clive Coleman said the debate was a "finely-balanced issue for the criminal justice system and has been kicking around for quite a long time".
"But now there is a real motor, if you like, with this petition and these very high profile individuals," he said.
Earlier on Monday Mr Gambaccini warned of a "false allegation crisis". The BBC DJ was arrested over sexual abuse allegations in 2013 but the case was dropped a year later.
Mr Gambaccini told Radio 4's Today programme: "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, 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".
Katie Russell, national spokesperson for Rape Crisis England and Wales, said giving suspects of sexual offences different treatment to suspects of other offences would "inevitably reinforce the public misconception... that those suspected of sexual offences are more likely to have been falsely accused".
Meanwhile in an open letter, Sarah Green and Rachel Krys from the End Violence Against Women Coalition asked Sir Cliff and the group to reconsider its call, calling it "grossly misdirected".
They said the harm that falsely-accused people feel is "not of the fact of being named but of terrible media representation of sexual violence cases, accompanied by a collective failure to uphold the presumption of innocence".
Professor Claire Mcgourlay, from the criminal justice centre at the University of Manchester, told the BBC News channel she could see both sides of the debate, but added if "there is anonymity in sexual offence cases, then I don't see how we should be distinguishing between these case and other cases".
Both defendants and complainants in rape cases were granted anonymity in 1976, but Parliament repealed anonymity for defendants 12 years later.
It was argued then 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.