Switzerland has blinked first in a standoff with the EU that mirrors the UK’s Brexit debate on the critical trade-off between free movement and a special trade deal with the bloc.

The Alpine republic voted narrowly to impose EU immigration quotas in a 2014 referendum that must be implemented by next February, but Brussels has said any cap would deny Switzerland its privileged access to the single market.

With talks between Bern and the EU commission due to resume on 19 September, Swiss ministers have welcomed a parliamentary panel’s plan to give preference to local people in job hires rather than impose unilateral quotas on foreigners.

It is not yet clear that the compromise, which must be debated by the full parliament, will win EU approval. But it represents at least a potential way out of the corner into which Switzerland has painted itself.

Any “major concession” by the EU, which has not budged from its stance that Switzerland must respect free movement rules or lose trade benefits, was plainly “unrealistic” following Britain’s exit vote, the justice minister Simonetta Sommaruga told the Neue Zürcher Zeitung.

Both Swiss and EU officials had previously said the UK referendum result had “complicated” the talks between the two sides, since any EU compromise with Switzerland would be almost certain to fuel similar demands from Britain.

All main political parties have supported the proposal, with the exception of the rightwing Swiss People’s party, which denounced it as a betrayal of voters who backed annual limits on foreigners’ residency and working rights.

Sommaruga said she believed a bill that encouraged Swiss employers to “fill open jobs first of all with suitable workers from Switzerland” could reduce immigration and comply with EU freedom of movement rules.

The economy minister and Swiss confederation president, Johann Schneider-Ammann, who will meet the EU commission chief Jean-Claude Juncker in Zurich later this month, said the plan could allow the government to “meet its constitutional obligation to manage immigration, without violating its EU agreements”.

Switzerland’s relations with the EU are governed by a set of multiple bilateral treaties that give it privileged access to much of the single market and are linked by a “guillotine clause” – if one treaty is breached, they all collapse.

Neither side wants that to happen: the EU takes more Swiss exports than any other market, and Switzerland is the EU’s fourth-largest trading partner. About 1 million EU citizens currently live in Switzerland.

But in a vote with a striking resemblance to Britain’s, the populist, Eurosceptic SVP called for and, against all establishment expectations, won the 2014 referendum, with 50.3% of voters – in a country whose population is almost one-quarter foreign – demanding immigration quotas.

As a result, the country not only finds itself threatened with exclusion from the EU’s single market, with potentially dramatic economic consequences, but has already been ejected from the EU’s science research programme, Horizon2020, and the Erasmus student exchange programme.

It has one further possible solution to its dilemma. A petition calling for a second referendum that would allow voters to make an explicit choice between imposing immigration controls on EU citizens and maintaining Switzerland’s special trade deal with the bloc has gathered enough signatures to trigger a new plebiscite.

The draft legislation unveiled late last week would “severely reduce” the attractiveness of hiring people from abroad, the parliamentary committee said, by favouring people – including EU citizens – already living in Switzerland.

If parliament and the EU do not approve it, the government is obliged to call a second referendum – the consequences of which would, this time, be rather clearer. It would be watched with interest in Britain.