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.

The most 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, the BBC has been told.

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

It comes after the two candidates for the Conservative leadership said the government had questions to answer about the new charges.

Axel Rudakubana, 18 – who is accused of murdering three young girls in Southport – is facing two further charges, including one under the terrorism act.

On Tuesday he was charged with production of a biological toxin contrary to Section 1 of the Biological Weapons Act 1974.

He has also been charged with possessing a PDF document of a kind likely to be useful to a person committing to or preparing an act of terrorism, contrary to Section 58 of the Terrorism Act 2000.

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.

To charge someone under the Biological Weapons Act, the Crown Prosecution Service has to obtain consent from the government’s law officers – the attorney general or solicitor general.

The BBC has been told that in this case, consent was requested in recent weeks, and granted “within days”.

The teenager had been due in court in Liverpool for a pre-trial preparation hearing last Friday, 25 October.

That was postponed in order for all the charges to be dealt with together at Westminster Magistrates Court, where he will appear on Wednesday 30 October.

The charging decision and its timing were a matter for the CPS, a government spokesperson added.

It comes after the two candidates for the Conservative leadership raised questions about the new charges.

Robert Jenrick suggested that information was being “concealed” from the public.

“We were told for months that this was not a terror-related incident, and yet we have learnt that this individual, the suspect, was allegedly reading al-Qaeda manuals and had access to dangerous substances like ricin,” he said.

“Given the scale of public interest, I think it is an important question to be asked, why was this information not put into the public domain sooner? So I’m asking the public authorities and the prime minister, what did they know, when did they learn it, and why was the decision taken not to be more honest and transparent with the public.”

Meanwhile Kemi Badenoch has suggested there are “serious questions to be asked of the police, the CPS and also of Keir Starmer’s response”.

She has not elaborated on what those questions are, suggesting they should be asked in Parliament.

The police say it is “certainly not the case” that they have been keeping things from the public. It would be highly unusual for them to release details of a live police investigation.

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

The new charges do not mean the Southport attacks are being treated as a terrorist incident.

Possessing a document that could be useful in preparing an act of terrorism is an entirely separate offence.

To be labelled as terrorism, the attack would have to be an attempt to advance a political, religious, racial or ideological cause. But it is not clear what possible motivation there might have been.

Authorities are urging people not to speculate, as it could jeopardise the entire court case.

Home Secretary Yvette Cooper said: “These additional charges will undoubtedly be distressing for people in Southport.

“The most important thing is to get justice for Bebe, Alice and Elsie and their heartbroken families, and all those affected by the attack and nobody should put that at risk.

“The police and prosecutors have an important job to do in their investigation, pursuing every avenue and taking the action they need to ahead of the trial.

“We must support them and ensure that everything possible is done to deliver justice.”