The TV presenter’s outburst comes after journalist Carole Malone, a Leave supporter, branded Remain voters “pessimists”.
Speaking on Sky News’ debate show The Pledge, she said Brexiteers “believe that Britain is great”.
“The thing that separates Leavers and Remainers for me, and you probably know that I’m a Leaver, is that Leavers are very optimistic,” she said.
“We’re very hopeful and we believe that Britain is great. We believe that anything we want to achieve, we can.
Nick Ferrari and Rachel Johnson clash on The Pledge
The first aim of the EU is to make sure Britain’s worse-off out than in, but hey, at least we know now – Brexit really does mean Brexit
“Remainers on the other hand, seem to think that Britain is this hopeless, weak little country that can’t survive without the prop of the European Union.”
Johnson, the sister of Leave campaigner and Foreign Secretary Boris Johnson, said those on the Remain side were injecting “reality” into the debate.
“It’s not just mere pessimism, it’s also a bit of reality,” she said. “Yesterday, what happened Carole? HSBC, UBS, Goldman Sachs all announced that they are moving their thousands of jobs to Frankfurt.”
However, LBC host Ferrari had heard enough and interrupted Johnson.
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Nick Ferrari and Rachel Johnson clashing over Theresa May's Brexit speech
“Google headquarters – London. Snapchat headquarters – London,” he blasted. “More Rolls-Royces being sold in Britain than ever before. Unemployment up.
“You’re talking utter cobblers, utter pessimistic cobblers. She’s nailed you. She’s nailed you completely. Utter, utter cobblers!”
He wrote: “Britain has chosen a hard Brexit. May's clarity is welcome—but the days of UK cherry-picking and Europe a la cart are over.”
And Johnson said: “Many of Theresa May’s sentences began ‘I want’ as if a bespoke deal for Britain is already on the table and simply ours for the taking – cherries, cakes, whatever’s on or off the menu, I’m afraid she’s being too greedy.
“And the first aim of the EU is to make sure Britain’s worse-off out than in, but hey, at least we know now – Brexit really does mean Brexit.”