Most Swiss people oppose a referendum campaign launched by the far right to end the free movement of citizens from the EU, according to a poll.

The referendum drive reflects unease with the influx of foreigners, who account for a quarter of the Swiss population. Imposing limits on EU citizens, however, would violate bilateral accords that enhance Swiss access to the single market, the lifeblood of the export-led Swiss economy.

A binding referendum is expected in May on whether Switzerland should take back unilateral control of immigration, if necessary at the cost of abrogating the free-movement pact that took full effect in 2007.

The vote was put on the agenda by the far-right People’s party, which is the largest in parliament and has two of seven seats in the federal cabinet.

The referendum under the Swiss system of direct democracy is billed as Switzerland’s “Brexit moment”.

A Tamedia online survey of about 11,000 people across the country found that 58% were against the idea, 35% approved and 7% had no opinion. It had a two-point margin of error.

Battling the referendum campaign is a priority for the Swiss government, which has struggled to put relations with the EU on a new footing.

Brussels wants the Swiss to endorse a new treaty that would have Bern routinely adopt single market rules and create a more effective platform to resolve disputes.

The Swiss government has dragged its feet for months while it tries to forge a domestic consensus on how to proceed, annoying Brussels and triggering a row over cross-border stock trading.

The treaty ran aground as a result of opposition that spanned the normally pro-EU centre left to the anti-EU far right. Critics say the pact infringes Swiss sovereignty to the extent that it would never get through parliament or pass a referendum.

The Tamedia poll found that 39% of respondents wanted the treaty renegotiated, 24% wanted it signed quickly and 24% wanted it rejected entirely.

Swiss voters backed quotas on EU immigration in 2014, but parliament avoided a crisis with Brussels by instead giving hiring preference to people registered as unemployed in Switzerland. This angered the People’s party and led to the referendum push.