The media should be banned from naming suspects, such as Sir Cliff Richard and Paul Gambaccini, unless and until they are charged with an offence, a committee of MPs has recommended.

The Commons home affairs select committee says all suspects should have the same right to anonymity that already protects victims of alleged sexual offences, including rape.

The MPs say names of suspects should only be released “for policing reasons” and then in a formal way: “There needs to be zero tolerance on the police leaking information on a suspect in an unattributed way. It is in the interests of the police, post-Leveson, to demonstrate the level of public distrust that has built up over the informal relationship between the police and the media.”

They say the number of celebrity suspects arrested as part of Operation Yewtree – the Jimmy Savile-related historical sex offences investigation – and the rise of social media, which has the potential to “amplify the reputational damage done by naming a suspect”, means it has become a matter of public debate.

The move is likely to meet strong criticism from police, who resent accusations that they routinely leak names that reach the public domain through other means. Nevertheless, the Metropolitan police commissioner, Sir Bernard Hogan-Howe, told the MPs’ inquiry that he supported granting accused people anonymity until charge.

Keith Vaz, the committee chairman, said that hearing of Gambaccini’s “12 months of trauma”, during which he was on police bail until being cleared, had persuaded him that suspects deserved anonymity.

“Police use of the ‘flypaper’ practice of arresting someone, leaking the details and then endlessly re-bailing them in the vague hope that other people come forward is unacceptable and must come to an immediate end,” said Vaz.

“It is inexcusable that information about suspects is released to the media in an informal, unattributed way. We have seen how destructive this can be to a person’s livelihood, causing irreparable reputational damage and enormous financial burden. The police must advocate zero tolerance on leaking names of suspects to the press before charge.”

The committee’s recommended ban follows evidence they heard about the media coverage of last year’s police search of Sir Cliff Richard’s home after details were leaked to the media. They also heard from the Leveson inquiry on the media impact of leaking the name of Christopher Jefferies, who was wrongly linked to the murder of Joanna Yeates in Bristol.

The Association of Chief Police Officers justified the decision to name some suspects. “On rare occasions a senior investigating officer may choose to name an arrested person where there is a good policing purpose for doing so, for example, in order to encourage other people who may have been victims to come forward,” said chief constable Chris Eyre. “The media are often capable of identifying and naming an arrested person without assistance from the police. Where information is released by officers or staff without the appropriate authority this will be taken seriously and dealt with.”

The MPs also took evidence from Gambaccini about the impact of unlimited police bail on him. In the end, no further action was taken against the radio disc jockey, but not before he had lost £200,000 in income and legal fees after being suspended by the BBC.

The MPs’ report says an initial 28-day time limit should be introduced on police bail, with extensions needing to be signed off by senior officers and a court review every three months. The home secretary, Theresa May, earlier this week renewed her intention to reform the law on police bail. Senior officers oppose a limit, saying that every investigation follows a different path and a limit would be unhelpful and expensive.