Ms Malone called out the former Tony Blair communication chief after he claimed pro-Brexit supporters had said leaving the European Union would be “straightforward.”
The Brexiteer commentator exploded against Mr Campbell when he told her to “rabbit on” during their fiery exchange.
She said: “So patronising. That’s what you are famous for, patronising people.
“No one said Brexit would be straightforward, everyone said there would be problems initially. Show me the quote that says somebody said Brexit was going to be straightforward. and I’ll take it back and apologise.”
Pro-Brexit politician Nigel Farage suggested a second vote could help “silence” pro-Remain voters seeking to overturn the result of the EU Referendum.
But Ms Malone said Mr Campbell was being “incredibly rude” for questioning the will of the people, remarking a second vote would still not placate Remainers complaining about leaving the European Union.
She said: “What he, Farage, said was that another referendum would ‘silence the wingers and the whiners.’ But it wouldn’t because people like yourself believe you are right about Europe and nothing – even if there was another referendum and Leave won by another three or four percent – would silence the likes of you.
“What you are saying is that if Leave won a second time you would still fight to have this overturned again. If the people voted a second time to leave the European Union, you would still fight to overturn that.”
Mr Campbell defended his political view, telling the TalkRADIO host that British voters are “entitled to change their minds” on whether to leave the EU as details of the effects of Brexit emerge.
He said: “Normally, after a referendum in most countries around the world, no matter how divisive and bitter the arguments people tend to come together. This hasn’t happened. It hasn’t happened because people are becoming more worried about the consequences.
“If the people are allowed to make their own judgement on the deal that the Government finally secures and they decide that’s the future that they want then we’re out: there is no doubt about that. This year is probably the last chance they can revisit this.”