In Italy, restive regionalism and sporadic separatist pushes are nothing new. Just last week, activists in the north-eastern Veneto region held an unofficial referendum in which more than two million people – according to the organisers – voted for independence.

As familiar as it is, however, the secessionist spirit has never manifested itself in quite the way a small group of activists is advocating in Sardinia. Angered by a system they say has squandered economic potential and disenfranchised the ordinary citizen, they have had enough. They want Rome to sell their island to the Swiss.

"People laugh when we say we should go to become part of Switzerland. That's to be expected," said Andrea Caruso, co-founder of the Canton Marittimo (Maritime Canton) movement.

While many have dismissed the proposal as a joke, its supporters insist they are serious. "The madness does not lie in putting forward this kind of suggestion," said Caruso. "The madness lies in how things are now."

A ruggedly beautiful gem in the middle of the Mediterranean, Sardinia – one of Italy's five autonomous regions – has always had a strong identity of its own. DH Lawrence, visiting in 1921, described it as "belonging to nowhere, never having belonged to anywhere".

For a minority of Sardinians, independence remains the island's best chance for success. Caruso and Enrico Napoleone, the two 50-year-old school friends behind Canton Marittimo, disagree with them. After decades of keeping faith in Rome, they now believe that staying in Italy can do no good- but fear that going it alone could end badly, too.

The answer, they say, lies more than 1,000km to the north.

"Having good teachers is something which in life everyone considers positive. We don't educate our children at home; we try to find the best teacher in the school," said Caruso, a dentist from Cagliari.

"Why, when we have this mentality with our children, do we have to renounce it when talking of our people?

"We think of Switzerland as a good teacher who could lead us on a path of excellence."

As the 27th canton, Sardinia, so goes the argument, would bring the Swiss its miles of stunning coastline and untapped economic potential. Sardinia could retain considerable autonomy, while also reaping the benefits of direct democracy, administrative efficiency and economic wealth.

The fact that Switzerland is not in the EU is "definitely" a plus, say the activists. Like many Italians, they no longer believe in Brussels's ability to deliver the dream – both economic and cultural – they once thought it could.

Beyond some specific local grievances, their frustrations with inefficient public spending, complex layers of decision-making and intimidating bureaucracy can be heard throughout the country.

Napoleone, who runs a car dealership in Cagliari, said being a small businessman in Italy was "a continuous battle".

"It is fighting every day with a problem that the administration, the bureaucracy, creates instead of solves," he said.

Those in work are still the lucky ones, however. In the last quarter of last year, the unemployment rate in Sardinia was 18.1%, the sixth highest in Italy. According to Istat, the national statistics body, more than half of households described their economic resources as either "scarce" or "absolutely insufficient".

Wearied by a procession of four prime ministers in less than two-and-a-half years, the Canton Marittimo backers hold out little hope that the latest, the centre-left leader Matteo Renzi, will be able to do anything to fix the system.

Napoleone and Caruso concede that many of their gripes chime with those of Beppe Grillo, the comedian turned anti-establishment figurehead whose Five Star Movement (M5S) broke through in last year's elections.

But the M5S, they say, was just one expression of that disillusionment. Their plan is another.

In Switzerland, the proposal has been met with cheerful bewilderment. An online poll of 4,000 people asking, in German, "should we accept Sardinia?" produced a 93% yes vote. A Swiss television crew was in Cagliari last week asking the same question.

On home turf, however, it may be some time before Canton Marittimo achieves a popular consensus. The group has more than 3,000 "likes" on Facebook but has yet to prompt the Sardinians to descend on the piazza en masse.

Caruso, however, remains undeterred. "Perhaps I too would laugh at such a paradoxical idea, but we say: 'OK, laugh, but reason with us'," he said. "What we are saying is not utopia. It's common sense."