The issue has been the subject of fierce debate in a series of high-profile cases, including recently over the charging of two men – reported to be Afghan asylum seekers – over the alleged rape of a 12-year-old girl in Nuneaton.
Ms Cooper said: “We want to see greater transparency.
“We think it’s important.
“Let me give you an example of recent cases that we had on national security and terrorism cases, where the police released the fact that the suspects were Iranian at the point at which they arrested them.
“The Crown Prosecution Service released the fact that those who were being charged, what their immigration and asylum status was at the point of charge.
“So, we know it is possible to provide more information. We do think there should be greater transparency.
“But that’s why we’ve asked the Law Commission to accelerate its review into what information can be provided, especially, you know, if there are court cases or trials underway, so that we’ve got that proper advice and information.
“And we are also working with the College of Policing on revising the guidance, because we do think more information should be provided.”
The Southport atrocity committed by Axel Rudakubana in July last year was also marked by a focus on the suspect’s ethnicity and immigration status – with false rumours spreading online that he was a Muslim asylum seeker, fuelling the riots seen in the aftermath of the stabbings.
The same force, Merseyside Police, were more transparent when a car drove into crowds during Liverpool FC’s Premier League victory parade, saying they had arrested a “white British man”.
Emily Spurrell, Merseyside’s Police and Crime Commissioner, told Today in Rudakubana’s case the situation was complicated because he was under 18 when he was arrested, which created “huge challenges” about what could be said.
She said: “I think the police will always aim to be as transparent as possible, but they are limited because of their need to protect the criminal justice process.”
She acknowledged that “we live in a very different world now” to when some of the guidance was first drafted as rumours could spread quickly online and there were some “bad actors who deliberately circulate false information to serve a particular agenda”.
The Nuneaton case has led to fresh pressure on police over the information they make public.
Ahmad Mulakhil, 23, was arrested on July 26 and charged the next day with rape, according to Warwickshire Police.
He appeared at Coventry Magistrates’ Court last Monday and has been remanded in custody.
Mohammad Kabir, 23, was arrested in Nuneaton on Thursday and charged with kidnap, strangulation and aiding and abetting rape of a girl under 13, the force added.
He appeared at Coventry Magistrates’ Court on Saturday and has been remanded in custody.
Ms Cooper added: “What we want to do is to change the guidance and to make sure that there is greater transparency.
“In any individual case, of course, there will be operational decisions about when information can be released in a live investigation.
“We recognise that, however, we do think that the guidance needs to change. We need the Law Commission assessment, because we do think more transparency is needed.”
Asked at a press conference on Monday whether the police should release the names, addresses and immigration status of people after they have been charged with an offence, Mr Farage said: “What caused unrest on our streets after Southport last year was us not being told the status of the attacker.
“That led to crazy conspiracy theories spreading online.”
Pushed later on whether the details should be published, Mr Farage said: “I absolutely think that they should.”
At the same press conference, Mr Farage linked a perceived lack of information from police about what happened in Nuneaton to what happened in Southport last July, telling a Westminster press conference that he wanted to discuss a “cover-up that in many ways is reminiscent of what happened after the Southport killings last year”.
He later told the event: “It is not … in any way at all a contempt of court for the British public to know the identity of those who allegedly have committed serious crimes.
“I felt that in the wake of the Southport attacks, and I feel that ever more strongly today.”