Singer Sir Cliff Richard and DJ Paul Gambaccini have revived a campaign calling for suspects to have their anonymity protected by law unless they are charged.

Both men were falsely accused of historical sex offences and joined forces with pressure group Falsely Accused Individuals for Reform (Fair) to campaign for changes to legislation.

Sir Cliff, 81, won his privacy case against the BBC over its coverage of a South Yorkshire Police raid on his home in Sunningdale, near Bracknell Forest, in August 2014, following a child sex assault allegation.

The veteran star denied the allegations, he was never arrested and in June 2016 prosecutors announced that he would face no charges.

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Three years ago the pair said they wanted to “redress the balance” in the legal system as they launched a petition to see those accused of sexual offences remain anonymous until charged, saying this was needed to “protect the reputations of all innocent suspects, whether well-known or not, from the lasting stigma of a false sexual allegation”.

The group said the petition received 27,000 signatures before it “had to be abandoned” when the general election was called.

Now they are pressing the Government to include an amendment in the next criminal justice bill because they believe the “law on privacy provides inadequate protection”.

At a press conference in the House of Lords on Wednesday afternoon, the pair were joined by former Tory MP Harvey Proctor and barrister Hugh Tomlinson QC – also part of the Hacked Off campaign group – to make their case.

Fair want the amendment to make it an offence in England and Wales for someone to identify or publish information about another person being subject of an investigation “in respect of the alleged commission of a sexual offence” unless charged or if there is a court order permitting this.

The veteran star denied the allegations, he was never arrested and in June 2016 prosecutors announced that he would face no charges.

He told the audience of reporters and campaign supporters he has learnt “how desperate it is to be accused of something you never did. We just need to change it (the law) a little bit. It’s just a compromise”.

He added: “Every single one of us is innocent until proven guilty, so all we are asking is… that you are not named until you are charged.”

Mr Gambaccini – who was arrested in October 2013 over claims he sexually assaulted two teenage boys as part of Operation Yewtree set up in the wake of the Jimmy Savile scandal – called on parliamentarians to help “restore the reputation of this country as the most just nation on earth”.

The 73-year-old, a regular fixture on the airwaves for decades, spent a year on bail before the case was dropped.

Addressing concerns from opponents to the plan that anonymity before charge would hinder victims coming forward and police trying to build a strong case, he said: “If the police are professional, they can take the case they have been given … and they can judge it on its merits. They don’t need bandwagoners to do that.”

If the accused is believed by the courts to be a threat in the “present moment” they could be named, Mr Gambaccini added, citing the case of the black cab rapist John Worboys as one where this could apply.

Mr Proctor, who had his home raided and was publicly named during Scotland Yard’s doomed sex abuse probe Operation Midland into fabricated claims of a VIP paedophile ring in Westminster by fantasist Carl Beech, said the group was “united for a common cause to return fairness to our criminal justice system.”

The now 75-year-old spent more than a year facing accusations that he was a child murderer and rapist before he was finally cleared and the investigation was abandoned amid widespread criticism.

Fair was founded by Daniel Janner QC, after his father, the late Lord Janner of Braunstone QC, faced allegations of child sex abuse. The family of the former Labour peer have always maintained his innocence.

He said “significant progress” had been made with the campaign since it was launched, adding: “Although we are clearly supported by very high-profile personalities, our aim is to change the law for everyone.”

Sir Cliff and Mr Gambaccini later told the PA news agency they were “confident” the campaign would succeed, while Mr Janner added: “I’m convinced this legislation is going to go through”, adding that former justice secretary Robert Buckland had been supportive of the plans.