The clash, on BBC Radio 4′s Today programme, came as Badenoch tried to publicise a global investment summit she is taking part in at Hampton Court today.
Webb initially asked her about former home secretary Braverman’s ideas for bringing down immigration, as well as her successor Cleverly’s recent comments about the government’s Rwanda plan.
But Badenoch told him: “What I don’t want to do this morning, Justin, is comment on everybody else’s comments. I have my own work that I’m doing that you don’t seem to be interested in and I suspect that’s because it’s good news.
“I would actually like to talk about the good things the government is doing, not comment on what Suella said or comment on what James said - I actually have my own job and I’m doing quite a lot which I think your listeners are interested in.”
Badenoch was also unhappy after Webb pointed out that there have been five business secretaries since 2015, and the same number of prime minister.
He said: “In other words on the one hand you’re holding this big jamboree, this big party, on the other hand behind the scenes, the way that the British government interacts with inward investment is too chaotic. Do you accept that there do need to be substantial changes, not just a party?”
Badenoch hit back: “It sounds to me, Justin, like you’re saying we shouldn’t have any change of government at all because that would create turbulence. I completely agree with you.”
Interrupting, Webb said: “Maybe not so many ministers all the time.”
Badenoch said: “That’s something else out of my control. In fact, I believe you had one of the companies investing £5bn in this country and that question was put to them and they dismissed it.
“The fact of the matter is that we’re getting £30bn of investment today, that’s three times what we did two years ago, so clearly it hasn’t had an impact.”
She added: “The fact of the matter is that there is turbulence all around the world.
“What is odd is how in this country we keep acting as if this is something unique to the UK. We are providing stability, we are bringing investment, we are growing the economy.”