Leaving aside the fact it's a Daily Express article and was likely written with hysterical glee to bad mouth the EU, it mentions nothing of Italy leaving the EU, just some corners of its ... unconventional government proposing a parallel currency. Hardly the same thing, and unlikely to gain any traction. It's Italy, there'll be another government due in another 12 months anyway.
If anything, Brexit has shone a light on the harsh realities of leaving the EU, with many 'populist', anti-EU parties dropping "leave the union" from their respective manifestos. For all the bluster of Italy, Hungry et al, I don't believe they're foolish enough to take the plunge. Now if Brexit turns out to be some kind of economic miracle for Britain, let's return to this thread in 5-10 years, but until then, this kind of talk just feels like projection on the authors' part...