Sir Keir Starmer has said David Lammy “set out the facts” on mistaken prisoner releases “to the best of his knowledge” amid questions over what the justice secretary knew and when.

Speaking for the first time since it emerged two prisoners were wrongly freed from HMP Wandsworth, the prime minister also said the situation was “intolerable” and that he was “angry and frustrated”.

The Met Police announced on Wednesday afternoon that registered sex offender Brahim Kaddour-Cherif, an Algerian national, had been released in error on 29 October. He is still at large.

A few hours later it was revealed another prisoner, 35-year-old William “Billy” Smith, had been wrongly released on Monday – the same day he was convicted for multiple fraud offences and handed a 45-month jail term. He has since handed himself in.

Asked how the public can have confidence in the justice system, Sir Keir said: “Let me just say how angry and frustrated I am that these mistakes have been made in releasing people. They’re intolerable, and they shouldn’t be made.

“A lot of it comes from the burden and the strain on the system because of the failures of the last government. But I recognise it’s our job to step up and to fix this.”

Sir Keir went on to defend Mr Lammy’s handing of the saga, which comes a week on from the mistaken release of Ethiopian sex offender Hadush Kebatu, who has since been deported.

Mr Lammy declared on 27 October that stronger prison checks in light of the Kebatu fiasco would come into force immediately.

But on Thursday, he said those checks were not in place when Kaddour-Cherif was released two days later.

Asked whether he was being truthful last week or on Thursday, Sir Keir said: “David Lammy can speak for himself on that.

“I’m absolutely clear that he’s setting out the facts, to the best of his knowledge and that’s the right thing for him to do.

“But whatever the checks, it’s intolerable. So, we have to make sure that whatever changes are needed are made.”

Government sources have said the mistakes that triggered the release of Kaddour-Cherif happened at the end of September, before the new regime was put in place.

Meanwhile on Thursday night, the Ministry of Justice (MoJ) announced the rollout of “cutting-edge technology to more prisons” in order to reduce human error and modernise “the archaic processes that have led to mistakes”.

“These measures will build on the tough new checks that were brought in last month, and ensure governor oversight of all releases,” the MoJ said.

Mr Lammy, who is also the deputy prime minister, is facing further criticism for failing to reveal that he knew of Kaddour-Cherif’s release during PMQs on Wednesday, when he was filing in for Sir Keir who is at the COP summit in Brazil.

He was asked repeatedly by Tory leader Kemi Badenoch whether any more asylum seekers had been wrongly released since Kebatu and refused to answer the question. The news broke at the end of PMQs.

On Thursday, Mr Lammy said he did not have all the details in the morning and did not want to mislead the public.

He told broadcasters: “I took the judgment that it is important when updating the House and the country about serious matters like this, that you have all of the details.

“I was not equipped with all of the detail, and the danger is that you end up misleading the House and the general public.

“So that is the judgment I took. I think it’s the right judgment.”

But shadow justice secretary Robert Jenrick said: “David Lammy has either lied or has absolutely no clue what’s going on in his department.

“How can the public have confidence in the justice secretary when he can’t establish a timeline of events or answer basic questions?”

Kaddour-Cherif was serving a sentence at HMP Wandsworth for trespass with intent to steal, but had previously been convicted for indecent exposure.

It is understood he is not an asylum seeker but is in the process of being deported after he overstayed his visa.