The row over the sacking of Sir Olly, who was the senior civil servant at the Foreign Office, has dominated the past week.
It emerged his department had given Lord Mandelson security clearance for the top diplomatic job in January 2025, despite concerns being raised during the vetting process.
Lord Mandelson formally took up the role the following month, but was sacked seven months later over his ties to the late convicted sex offender Jeffrey Epstein.
At PMQs, Conservative leader Kemi Badenoch embarked on a series of questions to the prime minister over the evidence provided by Sir Olly.
She asked whether the PM stood by his statement that due process was followed in Lord Mandelson’s appointment, to which he replied: “Yes, I do”.
She said trying to get a job for Lord Doyle in the Foreign Office was “ridiculous”, adding: “He promised them [Labour MPs] probity; what he has given them is cronyism and an Old Boy’s Club where Matthew Doyle is being proposed as an ambassador.”
The Tory leader demanded Sir Keir’s resignation, saying Sir Olly had been sacked for the failures of the prime minister, adding he “did not follow due process – yet he told the House he had”.