Sébastien Bosson gazes from his farm outside Bulle in Switzerland towards the snow-capped Alps.

The picture-postcard view is now marred by a forest of giant cranes building a billion-franc Rolex factory on former pastures. A forlorn farmhouse sits inside the construction site, awaiting demolition.

Mr Bosson, 45, whose 70 Holstein cows supply milk to the local Swiss chocolate factory, said: “When we arrived here, you couldn’t see a thing. No buildings, nothing. Now look. It’s all built up.”

As his young son parks a toy tractor on the lawn, he wonders what the boy will inherit, asking: “What are we going to leave them? Concrete and tarmac, that’s what.”

Bulle, the capital of the Gruyère region, has become the unlikely front line of a vote that could blow up Switzerland’s relationship with the EU.

On Sunday, the Swiss will decide whether to approve a citizen-driven initiative called “No to a Switzerland of 10 million”, writing a hard population cap into the constitution.

The Right-wing Swiss People’s Party (SVP), the country’s largest, blames “out-of-control immigration” for overcrowded trains, rocketing rents and urban sprawl.

The question is one Britain knows well: can a country regain control of immigration without wrecking the model that made it prosperous?

A Yes vote will force certain actions. If Switzerland’s permanent population reaches 9.5 million before 2050 – up from about 9.1 million today – its government must reduce arrivals, above all for asylum, family reunification and non-EU immigration.

If 10 million is still breached, Switzerland could end free movement with EU countries altogether.

Yet asylum seekers account for only about 7 per cent of arrivals, and non-EU workers already face strict quotas. Most newcomers are European: Portuguese builders, French nurses, Italian waiters, German executives. Cap the population, and it is they who must ultimately be turned away.

Free movement is the price of Switzerland’s privileged access to the single market, the bargain Britain knows intimately. The two are bolted together by a so-called guillotine clause: knock out one pillar and the rest fall with it.

If it ends free movement, Switzerland risks being shut out of a market that buys 55 per cent of its exports, and ejected from the Schengen and Dublin agreements, with border posts back at Geneva and Ticino.

In a veiled threat, an EU official told The Telegraph: “The free movement of persons is a key component of our relations, and of the package we signed. It is on this basis that we will be monitoring the outcome of this vote.”

Eurosceptics, too, will be keeping a keen eye on the vote, as Europe’s migration debate swings to the Right.

Switzerland was cited during the Brexit campaign as proof that a country could prosper outside the EU while keeping single-market access. Now the Swiss are being asked whether to tear up the very arrangement that made it attractive to some Brexiteers.

Beat Jans, the socialist justice minister, has drawn the comparison himself. He said: “The British have experienced what it means to leave access to the single market and free movement. The majority now regrets Brexit. We must learn from this lesson.”

In France, Jordan Bardella, the National Rally (RN) leader, has pledged a referendum on immigration if his party wins power next year.

A senior RN source told The Telegraph that Switzerland – “Europe’s most democratic country” – was right to let citizens “regain control of migration policy”, and France would do the same after 2027.

Frank Furedi, the executive director of MCC Brussels, a think tank, said the Swiss vote was being watched closely by parties across Europe.

He said: “That’s because it asks the question Brussels most fears: who decides the future of a nation – its citizens, or a treaty system that treats borders as a technical inconvenience? What Brussels fears most is the voice of the people who frankly don’t share the views of the EU elite on many issues.”

He believes Brussels would make an example of the Swiss if they chose to end free movement.

The SVP’s posters are everywhere in Bulle. One shows cranes and office blocks, warning against a “Switzerland of 10 million”. The No campaign answers with a foreign waitress, “Without her, no café”, and a nurse, “Without her, no care”.

Xavier Alonso, a senior RTS editor, says the Yes posters trade on a myth. He adds: “In the Swiss story, it was the peasants who built the country’s prosperity.

“The truth is that Switzerland’s wealth was made in its cities, by its banks, multinationals, drugmakers and watchmakers. That is a long way from Heidiland.”

Nowhere does the Yes case make itself more vivid than Bulle. The town’s population has doubled since the early 2000s, to more than 27,500, with 44 per cent of residents now foreign.

Housing and schools are under pressure. The Rolex plant alone will bring 2,000 jobs. At 5pm, Mr Bosson says, cars queue for more than half a mile to leave the motorway.

The irony is that his milk goes to a chocolate factory owned by Nestlé, whose chief executive, Philipp Navratil, has warned against the population cap, saying Switzerland “has created the conditions that enable a global company like us to thrive”.

The initiative faces broad opposition across government, parliament and business, and employers and unions have called it a “chaos initiative”.

Mr Bosson said: “If we vote Yes, we’re labelled racist. That’s not the case. I even know Portuguese who told me they hope I’ll vote yes.” His father, Jean-Marc Bosson, 74, is blunt. Of the land around Bulle, he says simply: “They’ve eaten it all up.”

Bulle is striking because it sits on the “wrong” side of Switzerland’s Röstigraben, the divide between German and French-speaking Switzerland.

The SVP’s power base is rural, conservative and German-speaking; French-speaking Romandy leans Left and pro-EU. Yet here in Gruyère, the party’s arguments about traffic, schools and lost identity are landing.

Nicolas Kolly, an SVP MP and former Pontifical Swiss Guard, who grew up on a farm above Bulle, says: “We’re on a demographic runaway train. At some point, we need to slow down.”

The Rolex paradox is not lost on him. Bulle sold the luxury watchmaker more than 100,000 sq m of land for 31m Swiss francs (about £29m), he says, “precisely because we support this type of economy”.

His question is what follows the jobs: “Do we want villages with a village quality of life? Or urban centres everywhere?”

His opponents call that hypocrisy.

Marie-France Roth-Pasquier, a centrist MP and Bulle town councillor, says the town’s boom was driven first by Swiss families seeking cheaper homes inland, before foreign workers arrived to staff its hospitals, care homes, hotels and building sites.

She says: “We want the workforce, but we don’t want too many of them. We’d like to choose our own. We’re a small island in the middle of Europe.”

In the cobbled old town, locals are split.

Jacqueline Pasquier, 73, will vote Yes: “We need foreigners, but we need to regulate. In 2014, we voted for that. They simply didn’t legislate.”

Her husband, Luc Pasquier, 74, a retired engineer, will too, “but just to shake things up – they tell us to vote No and offer no solutions”. David Hofer, 35, an IT worker, sees something uglier, calling it “a border blockade disguised as a sustainability initiative”.

The men building the Rolex factory know where they stand.

Santos Neves Serafin, 53, a metalworker who has lived in the town for 16 years, says: “Bulle can’t do without us Portuguese. They need us. Most foreigners who come here work. They don’t ask for handouts.”

Laurent Wehrli, a conservative who chairs the Swiss parliament’s foreign affairs committee, warns that renegotiation with Brussels would yield a worse deal.

“We’ll never be able to renegotiate as well or as thoroughly as we’ve been able to do so far,” he says.

For the Eurosceptic Right, there is a bigger issue.

Mr Furedi, of MCC Brussels, says: “Brussels learned from Brexit that punishment has pedagogical value. The treatment of Switzerland may become another demonstration case, a reminder that sovereignty is permitted only so long as it is not exercised.”

The latest poll puts No ahead at 52 per cent, but the result on Sunday will come down to mobilisation. Italian-speaking Ticino, which is nearest the migrant routes, leans Yes hardest.

In a mountain chalet overlooking Lake Gruyère, Fabien Kolly, 40, makes the region’s eponymous cheese the old-fashioned way, stirring milk in a copper cauldron over a wood fire before pressing the curds into wheels.

Below, he can see Bulle expanding.

One of six brothers – two of them politicians, including Nicolas Kolly – Mr Kolly is careful to separate his Yes vote from hostility to foreigners. He says: “We must respect people. Those who come must be well looked after.”

For him, the vote is about whether direct democracy still means anything if Brussels can overrule it.

He says: “When you have direct democracy, more Europe means less direct democracy. If we vote and it isn’t implemented because Europe says no, then democracy is useless.

“In Switzerland, every citizen has the right to vote. Sometimes we vote on the most trivial things, like cow horns. Sometimes on important matters. But democracy is something sacred to us.”

His metaphor is agricultural: “If I ask my farm to produce 3 per cent more each year, it isn’t possible. The land becomes exhausted. You need growth, but qualitative growth, not just quantitative.”

He fears Switzerland is becoming “a Singapore” and asks whether it can “hold on to a tiny bit of our Swiss quality of life, even if it means a bit less money”.

Inside the chalet hang cowbells from 1940 that belonged to Mr Kolly’s great-grandfather. He still uses them with the herd. “We know where we come from,” he adds. “We’d like to know where we’re going.”