GENEVA (Reuters) - A shock referendum result demanding controls on European Union migration has created a serious headache for politicians, who must do the people’s bidding without jeopardizing access to the single market.

An assistant talks to migrants in a Swiss Federal refugee center, set-up in a tank hall on the army base in Thun, Switzerland March 22, 2016. REUTERS/Ruben Sprich

Not Britain: Switzerland.

Home to more than a million EU citizens, Switzerland voted on Feb 9, 2014 to impose quotas on migration, potentially ripping up a bilateral deal with the EU on free movement of people. It could trigger a “guillotine clause” cancelling six other bilateral agreements, including on air transport, road, rail and agriculture.

The government sees few ways out and, in what could be a warning to Britain, may have no choice but to ask voters to reconsider. Though even that is difficult.

Switzerland is one of the models some supporters of Britain leaving the European Union have pointed to of a European economy that thrives outside of the EU. But in 1999, to negotiate access to the European single market, it had to agree to bilateral deals that allow free movement of workers from EU countries.

European leaders say they will demand similar “free movement” conditions if Britain is to retain easy access to the EU market, a position that British officials acknowledge makes it difficult to deliver the limits on migration that voters want while also keeping the free trade businesses need.

As in Britain, voters defied the advice of their government to deliver a narrow victory to a referendum campaign led by right-wing populists.

The Swiss referendum was backed in rural areas with few migrants, and carried with 50.3 percent of the vote, upsetting businesses and creating an unexpected dilemma for the government. Switzerland now has until February to implement the binding result.

“Right now we are in a situation that is both delicate and paradoxical,” Swiss negotiator Jacques de Watteville told an audience of Swiss bankers earlier this month, before the Brexit vote.

Foreigners make up a quarter of the population of the neutral Alpine country, which despite being outside the EU is inside its Schengen zone of border-free travel. Three hundred thousand workers commute into Switzerland across borders from France, Germany and Italy every day.

NEW REFERENDUM?

Swiss politicians now appear to face a choice of passing legislation that the EU will reject, abrogating their agreements with the EU unilaterally, or hoping that the 2014 vote will get overturned by a new referendum.

“I don’t see any possibility for the EU to give anything to Switzerland,” said René Schwok, a professor at the University of Geneva and author of books on Swiss-EU relations.

The referendum has already resulted in Switzerland being dumped from Europe’s “Erasmus” university exchange program. Once the government passes legislation to implement it, the guillotine clause would end a range of other bilateral agreements, having far wider impact.

A campaign to overturn the 2014 referendum is already underway, but it would require a majority of Switzerland’s 26 cantons to agree, as well as the population, which means it is unlikely to succeed, Schwok said.

Some in Britain are closely watching the Swiss case for the lessons they can learn. Remain campaigners say it shows that the victorious Leave side may not be able to deliver its promises.

“It’s not at all clear that Switzerland is going to achieve the objectives that it has set out,” said British Foreign Secretary Philip Hammond, who campaigned to remain in the EU against a Leave campaign also led by figures from his ruling Conservative Party.

“There are some of my colleagues in the Conservative party at the moment saying things like ‘It’ll be straightforward to agree access to the single market and there’ll be no need to have freedom of movement,’” he told BBC radio this week.

“I’m afraid they are simply betraying a lack of understanding of the political realities in the European Union. It will be much more complicated than that.”

De Watteville, the Swiss diplomat charged with finding a solution to the EU problem, said whatever solution is found, the Swiss will probably have to return to the ballot box.

“In the end, it’s going to be up to the Swiss people to decide, because in any scenario, it’s very likely that a referendum will be announced by one side or the other,” he said.