On Tuesday evening, the House of Commons voted not to refer the prime minister to the Privileges Committee by 335 votes to 233.
The majority of Labour MPs voted against the motion, following a No 10 operation to rally support for the prime minister.
Sir Keir has rejected claims he misled the Commons about the vetting process for Lord Mandelson, who was appointed as the UK’s ambassador to the US but sacked seven months into the job.
Badenoch said the prime minister had been reduced to “begging” his MPs for their support in the vote and drew a contrast with the weeks following the 2024 general election when she said the government benches were “full of sycophantic questions from adoring new MPs”.
“This government is like a bad episode of Game Of Thrones,” she said, and in a reference to Greater Manchester Mayor Andy Burnham, added: “His own people have turned against him and all the while, the prime minister is holed up in his castle, wetting himself about a visit from the King in the North.”
The Conservative leader argued that the UK could not defend itself because too much money was being spent on welfare and the prime minister was unable to cut benefit bills because he had “squandered all his political capital saving his own skin”.
The prime minister replied that the government was increasing defence spending to its highest level since the end of the Cold War.
He also said the government had introduce the youth guarantee aimed at helping young people into work.
Referring to the Privileges Committee vote on Tuesday, Sir Keir said that while he had been chairing a meeting on the war in the Middle East, Badenoch had been engaged in “a desperate, baseless political stunt”.
Also during PMQs, Badenoch seized on rumours in Westminster of a government reshuffle in the wake of next week’s elections.
The Conservative leader asked if the prime minister would “listen to the country and reshuffle the Chancellor?”
Sir Keir did not directly answer the question, highlighting falling interest rates before the war in Iran.
But the PM’s failure to rule out sacking Rachel Reeves prompted Badenoch to declare the Chancellor was “toast”.
Last year Downing Street said Reeves will remain in her role “for the whole of this Parliament”. In a briefing to journalists after PMQs, the prime minister’s political secretary tried to hose down rumours about the Chancellor’s position.
“The position remains unchanged,” he said.