Ms Badenoch, who previously served as business secretary, also used her speech to warn that high migration was putting pressure on housing.
He said Labour’s plans to fast-track applications for 90,000 asylum seekers previously earmarked for deportation to Rwanda would require more homes.
The former cabinet minister also warned Rayner that he would have to confront rising “sectarianism” after Labour lost several seats to pro-Palestine candidates.
“In this election we saw independent MPs win seats over Labour on the back of sectarianism and integration, failures that Labour continually denies exist, while we saw riots in Leeds,” he added.
Ms Rayner told the Commons that Britain was being held back by its “housing crisis” and criticised the Conservatives for leaving the new government “a mountain to climb”.
He said new home completions would hit their lowest level since the Second World War as the Conservatives left behind a “chronic housing shortage”.
But he also sought to play down concerns that Labour is planning to impose huge new housing developments on local communities without their consent.
“It is only fair that local people have a say in what kind of houses are built and where, because our aim is not to build big, but to build well,” he said.
“We want to see more local plans and more engagement with local leaders to build the homes people want in their area, working alongside them.”
His comments came after Sir Keir said that under his government locals would only have a say in “how, not whether” new homes are built.
