Cliff Richard has said people still think there’s “no smoke without fire” over false sexual assault allegations, as he launched a petition to give anonymity to suspects before they are charged.

The singer, whose home was raided by police in 2014 over an unfounded sexual abuse claim, said his aim was a “rebalancing of the justice system” and that suspects should be named only in “truly exceptional circumstances”.

Speaking at a launch event in Victoria Tower Gardens in Westminster on Monday, Richard said he felt his reputation “was in absolute tatters” after a South Yorkshire police investigation into him was dropped in 2016.

The singer has thrown his weight behind a parliamentary petition by the campaign group Falsely Accused Individuals for Reform (Fair) alongside the DJ Paul Gambaccini – who also faced sexual abuse claims that were later dropped.

The petition needs to be signed by 100,000 people to be considered for debate in parliament. By Monday afternoon signatories stood at 8,500.

Rape Crisis, an umbrella body for rape crisis centres across England and Wales, said false allegations of sexual offences were rare and the focus should be on improving the criminal justice system for victims and survivors.

Alleged victims of sexual offences are granted lifelong anonymity, while suspects can be named at any time during an investigation.

Richard, who said he had been able to sleep for only about three hours a night in the years following the accusations made against him, said he believed some people still thought he was guilty.

“Despite no charges being brought against me, and despite winning my privacy case, I’m sure there’s still people who believe in that stupid adage ‘no smoke without fire’,” he said.

He successfully sued the BBC last year for breach of privacy after they broadcast footage of the raid on his Berkshire home, which was filmed from a helicopter.

Q&A What are the laws about maintaining anonymity in sex offence accusations? Show Hide All victims of rape and other sex crimes in England and Wales, including children, are automatically guaranteed anonymity for life from the moment they make a complaint that they are the victim of a sex crime. The law is different in Scotland, but the practice of respecting anonymity is the same. It is a criminal offence to publish the complainant's identity or any information that might lead to them being identified. People accused of rape and other sex offences can though be named. In the 1970s, anonymity for both rape complainants and defendants was put into law, though the anonymity for rape defendants was later repealed. The 2010 Coalition Agreement between the Conservatives and Liberal Democrats proposed re-introducing anonymity for defendants. However, after examining the issue to propose legislation, the government concluded that there was insufficient reliable evidence to justify a change in the law. Those in favour of changing the law say that the stigma of being accused of rape is such that it has a devastating effect on the life of people subsequently found to be wholly innocent. Against this is set the argument that naming the defendant is important in allowing other potential victims and witnesses to come forward. One suggested alternative has been ensuring the anonymity of defendants in sexual offence cases, unless a judge orders a case-specific exception.

While he suggested some sexual offence suspects should be named if they were deemed to be an imminent threat to the public, Richard added that the time between a suspect being charged and a court case beginning would allow further victims to come forward.

Gambaccini, who earlier warned of a “false allegation crisis”, was arrested in 2013 as part of Operation Yewtree over claims that he had sexually assaulted two boys. After he had spent a year on bail, the case against him was dropped. Operation Yewtree was set up in the wake of revelations about historic sex offences by Jimmy Savile.

Katie Russell, a Rape Crisis spokeswoman, said giving “exceptional treatment” to suspects would reinforce misconceptions “that those suspected of sexual offences are more likely to have been falsely accused than those suspected of other types of crime”.

Fair was founded by Daniel Janner QC, whose father, Greville Janner, was charged with 22 sexual offences. He was ruled unfit to stand trial and later died.

Parliament repealed anonymity for defendants in rape cases in 1988 after it was ruled that comparisons should not be drawn between rape defendants and victims.