Mr Clarke says reporting restrictions can damage public confidence in police
The government should review the Contempt of Court Act, the UK's former top anti-terror police officer says.
Peter Clarke said the law, designed to ensure fair trials by limiting reporting of cases, made it harder for anti-terrorism police to do their jobs.
He said if they could not fully explain their actions, it made it difficult for communities to have confidence in them.
The Criminal Bar Association disagreed with Mr Clarke, saying the law "should not constitute a problem" for police.
The Contempt of Court Act became law in 1981.
It says once someone has been arrested, any kind of publication that creates "a substantial risk that the course of justice... will be seriously impeded or prejudiced" is a criminal offence, regardless of intent.
This affects what the media can publish or broadcast and what the police can say.
Former attorney general Lord Goldsmith agreed with Mr Clarke's call, claiming the law "can damage confidence in the police" where it leaves them unable to properly explain their actions.
"For community relations and for people to be willing to report to the police they need to be satisfied that the police are acting sensibly," he told the BBC.
Mr Clarke headed the Metropolitan Police's Counter Terrorism Command until last year.
In an exclusive interview with BBC Radio 4's The World This Weekend, Mr Clarke, who is the former national co-ordinator for terrorism investigations, said he believed there was a link between "the application of the act and the potential effectiveness of counter-terrorism policing".
He said: "It's fundamental to any type of policing that communities must have confidence in what the police are doing.
There seems to be a presumption that juries are not capable with dealing with the information that's put before them
"All too often, though, it's been two or even three years before we've been able to explain to communities why certain actions were carried out.
"If that happens, it's going to be far more difficult for those communities to actually have confidence in the police, to have the confidence to come forward with intelligence and information which could be absolutely vital."
In January 2003 the police raided a mosque in Finsbury Park, north London.
At the time, it had long been associated with extremists but, nonetheless, raiding a place of worship was controversial.
Peter Clarke said because of active ongoing investigations and the ensuing court cases, he was unable to give a full explanation for the raid until three years later.
He said he believed this had had an impact on policing.
"I know this is obviously controversial but it did mean that we actually had to skew the conduct of operations to take account of the sorts of criticisms that we'd been subject to but been unable to counter because of what we couldn't say about forthcoming cases," he said.
Mr Clarke fears that by not being able to paint a full picture for the public, the door can be left open to be exploited by extremists and the police are unable to respond.
He said: "There seems to be a presumption that juries are not capable with dealing with the information that's put before them, incapable of deciding whether something is probative or prejudicial to a defendant.
Police could not say why they raided a London mosque for three years
"Juries are the bedrock of our judicial system - we need to cherish them and, most importantly, we need to trust them."
Lord Goldsmith, who was attorney general at the time of the Finsbury Park raids, said any relaxation of the law would have to consider the "huge change in communications" that has occurred since it was drafted.
"We have global communications, which means that people get access to foreign media that is not controlled by the British Contempt of Court Act," he said.
"And you have the internet which gives a permanence to what would otherwise be temporary statement."
Lord Goldsmith said evidence from other countries suggested juries were much more affected by what happened in court than outside.
But because the Contempt of Court Act also banned any public discussion of jury room deliberations, it was currently impossible to do any real research to test that, he added.
The government has not responded to Mr Clarke's calls for a review, but says the Contempt of Court Act is designed to ensure that a fair trial can be held.
The chairman of the Criminal Bar Association, Peter Lodder QC, agreed and said he had not heard any other calls for a review of the act.
The police should deny false reports, but I don't think you need to do away with the Contempt of Court Act
Abdurahman Jafar Muslim Safety Forum
"The point here is that they should not publish anything which constitutes a substantial risk of serious prejudice to the conduct of the trial," he said.
"That is a high test and employing the words of those tests and using common sense, should not, in fact, constitute a problem."
Abdurahman Jafar, from the Muslim Safety Forum, which liaises with the police and British Muslims, said Mr Clarke was wrong.
He told the BBC that more information would only fuel the "media feeding frenzy" around these cases and lead to "an increase in isolation and criminalisation" within the Muslim community.
"What we've seen is huge amounts of publicity when people are arrested but when the individuals were either acquitted or the charges dropped there is absolutely no publicity whatsoever," he said.
"The result of that is that the wider public feel as though Muslims per se are a community of terrorists."
Mr Jafar added: "The police should deny false reports, but I don't think you need to do away with the contempt of court act."
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