“We learned yesterday the Education Secretary knew well in advance that there was a problem with the algorithm,” Sir Keir told the Commons.
“So a straight answer to a straight question please Prime Minister: when did the Prime Minister first know that there was a problem with the algorithm?”
But the Prime Minister sidestepped the question and instead asked Sir Keir to congratulate students on receiving their grades.
“As a result of what we learned about the tests, the results that had come in, we did institute a change, we did act,” said Mr Johnson.
“The students, the pupils of this country now do have their grades and I really ask (Sir Keir) whether he will join me in congratulating those pupils on their hard work and whether he agrees with me that they deserve the grades they’ve got.”
The Labour leader hit back by accusing Mr Johnson of being “just tin eared and making it up as he goes along”.
Sir Keir again put the question to the Prime Minister saying: “He either knew of the problem with the algorithm and did nothing or he didn’t know when he should have.”
He added: “He’s fooling nobody, even his own MPs have run out of patience.
“It’s the same problem every time – pretending the problem doesn’t and brushing away scrutiny. This has got to change.”
Sir Keir also challenged the Prime Minister about his decision to cancel a meeting with a group of families bereaved by Covid-19.
“Before the recess, I asked him if he would meet with the Covid-19 Bereaved Families for Justice group,” Sir Keir told ministers.
“I had the privilege of meeting the families on July 15. They gave me incredibly moving accounts of how Covid-19 had taken their loved ones from them.
“On Sky News last week the Prime Minister was asked if he would meet the families and he said and I quote ‘Of course I will meet the bereaved, of course I will do that’. But yesterday they received a letter from the Prime Minister saying that meeting them was now ‘regrettably not possible’.
“The Prime Minister will understand the frustration and the hurt of those families that he said one thing to camera and another thing to them.”
Responding, Mr Johnson said: “It’s absolutely typical of him that he should frame it in that way… Of course I would be very happy to meet the families of the bereaved and sympathise deeply with all those who have lost loved ones throughout this pandemic and we all feel their pain and their grief.
“It turns out that this particular group that he refers to are currently in litigation against the Government and I will certainly meet them once that litigation is concluded.”
Sir Keir was joined by ministers who urged Mr Johnson to the furlough scheme beyond October.
The Labour leader warned: “The jobs of millions of people are at risk, the longer he delays, the more they’re at risk, so will he act, finally get this decision right and commit to extend the furlough for those sectors and those workers that desperately need it?”
SNP Westminster leader Ian Blackford added: “With the clock ticking for struggling businesses and workers, will the Prime Minister commit today to extend the job retention scheme beyond October?
“Or is his Government making the political choice to accept levels of unemployment last seen under Thatcher in the early 1980s?”
But the Prime Minister defended his Government’s approach to the furlough scheme, saying it had already cost the UK £40 billion.
“Members opposite of all parties seem to want to extend the furlough scheme which has already cost this country £40 billion… supported 11 million people, but after all keeps them in suspended animation and prevents them from going to work,” said Mr Johnson.
“What we want to do is get people back to work and that’s why I hope he (Mr Blackford) will instead support our Kickstarter scheme to get young people into jobs and support them in those jobs.
“How much better is that than languishing out of work?”