The prime minister has criticised both Conservative leadership candidates for casting doubt on the police and government’s response to the Southport attack that left three young girls dead.

Tory leadership hopeful Robert Jenrick has suggested information on the attack was “concealed”, while his rival Kemi Badenoch argued that the government, police and prosecutors “have questions to answer”.

This follows the revelation 18-year-old Axel Rudakubana, who is accused of murdering the three girls, was charged with two further offences – including one under the Terrorism Act.

Sir Keir warned MPs they “can either support the police in their difficult work” on the Southport case or “undermine” it.

During his weekly Prime Minister’s Questions session, Sir Keir told a packed House of Commons: “It is important police and prosecutors are able to do their difficult job.

“All of us have a choice to make, including those running to be Conservative leader, they can either support the police in their difficult task or they can undermine the police in their difficult task, and I know what side I am on.”

Badenoch was in the Commons to hear the comments.

Sir Keir was responding to a question from Reform UK’s deputy leader Richard Tice, who called for the police to be more open about investigations.

Reform UK leader Nigel Farage faced criticism after the Southport killings for questioning the police’s assessment of the attacks.

Following the revelations about the extra charges against Mr Rudakubana, Farage released a video claiming “perhaps I was right all along”.

On Wednesday, Mr Rudakubana appeared in court charged with production of the poison ricin and possession of a military study of the Al Qaeda training manual, an offence under terrorism legislation.

Counter Terrorism Police are not currently treating the Southport attack itself as a terrorist incident.

The teenager had already been charged with the murders of Bebe King, six, Elsie Dot Stancombe, seven, and nine-year-old Alice Dasilva Aguiar who died at a Taylor Swift-themed dance class on 29 July.

Following reports of the new charges, Jenrick told ITV News he wanted answers on “when the prime minister knew”.

“The state should not be lying to its own citizens,” he said.

Asked if he thought the state had lied, Jenrick said: “We don’t know the reason why this information has been concealed.

“Why has it taken months for the police to set out basic facts about this case that it is reasonable to believe were known within hours or days of this incident occurring?”

In a social media post Badenoch said there were “serious questions to be asked of the police, the [Crown Prosecution Service] and also of Keir Starmer’s response to the whole situation”.

She said: “Parliament is the right place for this to happen.

“While we must abide by the rules of contempt of court and not prejudice this case, it is important that there is appropriate scrutiny.”

The BBC understands senior figures in government first became aware of the possibility of new charges against the suspect in the Southport murders in the past few weeks.

A spokesperson for the prime minister said it was “not correct” to say the government had been involved in withholding facts from the public.

The CPS said it has taken time to bring the charges because this was a “lengthy and complex investigation”.

Ahead of PMQs, House of Commons Speaker Sir Lindsay Hoyle warned MPs of the risk of seriously prejudicing criminal proceedings by commenting on the investigation in the Commons.

While members might be frustrated at not being able to comment he said: “More importantly at the heart of this case are three young girls.

“We all went to see justice for them and others affected by this appalling incident.”

The day after the Southport attack, thousands attended a peaceful vigil in the town, but a separate protest later turned violent outside a mosque.

This sparked a wave of protests across many towns and cities in the following days, leading to violence and rioting, particularly against asylum centre hotels.

More than 1,000 people have been arrested, and hundreds have been charged and sentenced to jail.