There should be “greater transparency” around the immigration status and ethnicity of crime suspects, and guidance for police forces on when to disclose this information “needs to change”, the home secretary has said.

Reform UK leader Nigel Farage has called on police to release details of two men arrested in connection with the alleged rape of a 12-year-old girl in Warwickshire.

The men are reportedly Afghan nationals but police have not confirmed this.

Asked if she believed that kind of information should be in the public domain, Yvette Cooper told the BBC: “We do want to see more transparency in cases, we think local people do need to have more information.”

On Monday, Farage said he “absolutely” believed that such details should be released.

Warwickshire Police has previously said once someone is charged with an offence, the force follows national guidance that does not include sharing ethnicity or immigration status.

Speaking to BBC Breakfast on Tuesday, Cooper said: “It is an operational decision about how much information can be revealed in the middle of a live investigation but we do want to see greater transparency.”

She later told BBC Radio 4’s Today programme: “We do think the guidance needs to change”.

She said the government had asked the Law Commission – an independent body which reviews laws in England and Wales – to speed up a review into “what the rules are” around what information can be released and when during a legal case.

“We’re also working with the College of Policing on strengthening and changing their guidance,” she said.

The two men accused of the offence in Warwickshire are: Ahmad Mulakhil, who has been charged with two counts of rape; Mohammad Kabir, who has been accused of kidnap, strangulation and aiding and abetting the rape of a girl aged under 13.

Mr Mulakhil, 23, appeared before magistrates in Coventry on 28 July, and Mr Kabir, also 23, appeared in court on Saturday.

Both were remanded in custody.

In a statement, Warwickshire Police and Crime Commissioner Philip Seccombe said: “It is essential to state that policing decisions – such as whether to release details about a suspect – must follow national guidance and legal requirements.”

He added that he would not speculate on the personal circumstances of those involved while court proceedings were active.

The Law Commission is conducting a review into what information or opinions someone should lawfully be able to publish after a suspect has been arrested.

Following a government request, it has agreed to speed up its reporting on the parts of the review that relate to what the government and law enforcement can do to counter misinformation, including where there are possible public order consequences of failing to do so.

An independent watchdog concluded in March that failure to share basic facts about the Southport killer led to “dangerous fictions” which helped spark rioting.

Jonathan Hall KC, the UK’s independent reviewer of terrorism legislation, said it would have been “far better” for the authorities to share more accurate detail on the arrest of Axel Rudakubana on 29 July last year.

He said the “ineffectual near silence” from police, prosecutors and the government after the attacks led to disinformation that sparked widespread rioting in the days after the attack.